# Differentiation and finding tangent

• Maatttt0
In summary, the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16) is (x + 1)3((x + 1)2x + 4x2).
Maatttt0

## Homework Statement

Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16)

## The Attempt at a Solution

dy/dx x2(x + 1)4

= (x + 1)3((x + 1)2x + 4x2)

= (x + 1)3(6x2 + 2x)

= (x + 1)3(2x)(3x + 1)

Subst. 1 into find grad.

(1 + 1)3(2)(3 + 1)

= 64

Seems wrong..

y - 16 = 64(x - 1)

y = 64x - 48

I think it's probably wrong, just so confused - can someone give me a hand please? Much appreciated

Maatttt0 said:

## Homework Statement

Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16)

## The Attempt at a Solution

dy/dx x2(x + 1)4

= (x + 1)3((x + 1)2x + 4x2)

= (x + 1)3(6x2 + 2x)

= (x + 1)3(2x)(3x + 1)

Subst. 1 into find grad.

(1 + 1)3(2)(3 + 1)

= 64

Seems wrong..

y - 16 = 64(x - 1)

y = 64x - 48

I think it's probably wrong, just so confused - can someone give me a hand please? Much appreciated

You should plug it into the derivative formula

$$f'(x) = \lim_{h \to 0}\frac{f(x+h) - f(x)}{h}$$

and put this into you Calculator...

and use the good old Tangent formula.

$$y = f(a) + f'(a)(x-a)$$ where you take the derivative at x = a.

Thank you for your reply, Susanne, it's just that I've never seen the tangent formula before :S

Also my homework is based around the idea of differentiating so I was wondering if I was going in the right direction :S

Maatttt0 said:
Thank you for your reply, Susanne, it's just that I've never seen the tangent formula before :S

Also my homework is based around the idea of differentiating so I was wondering if I was going in the right direction :S

You derivative is correct.

But you can use the definition of the derivative and graphical Calculator to check your result.

and your userage of the tangent formula looks to be okay too :)

Last edited:
Oo okay, thank you - just thought it was wrong considering the grad was 64 that's all.

Thanks Susanne for checking :D

## 1. What is differentiation?

Differentiation is a mathematical process used to find the rate of change of a function. It involves finding the slope of the tangent line to a curve at a specific point.

## 2. How do you find the derivative of a function?

The derivative of a function can be found using the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of any function by manipulating its terms and variables.

## 3. What is the difference between differentiation and integration?

Differentiation is the process of finding the derivative of a function, while integration is the process of finding the anti-derivative of a function. In other words, differentiation calculates the rate of change, while integration calculates the total change over a given interval.

## 4. How do you find the tangent line to a curve at a specific point?

To find the tangent line to a curve at a specific point, you must first find the derivative of the function at that point. The derivative represents the slope of the tangent line. Then, you can use the point-slope formula to find the equation of the tangent line.

## 5. Why is finding the tangent line important?

Finding the tangent line is important because it allows us to analyze the behavior of a function at a specific point. It helps us understand the rate of change of the function and how it is affected by different inputs. This information is crucial in many real-world applications, such as physics, economics, and engineering.

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