Finding Local Max, Min, and POI of y=-x^5+5x-6

[duki]

Homework Statement

a) Graph $$y = -x^5 +5x -6$$. Include coordinates of local max, min, and points of inflection. Indicate the behavior as x-> -infinity, x -> infinity.

b) Find in slope-intercept form the equation of the tangent line to the curve at x = 2.

Homework Equations

The Attempt at a Solution

a) I found that the critical numbers are 1 and -1. The POI is 0. As x->infinity the limit -> -infinity and vice versa. Coordinates are (1,-2), (0,-6), (-1,-10). I've also graphed it to match my findings.

b) I'm not sure what to do for this part.

Thanks for any help!

 

[rock.freak667]

Homework Statement

a) Graph $$y = -x^5 +5x -6$$. Include coordinates of local max, min, and points of inflection. Indicate the behavior as x-> -infinity, x -> infinity.

b) Find in slope-intercept form the equation of the tangent line to the curve at x = 2.

Homework Equations

The Attempt at a Solution

a) I found that the critical numbers are 1 and -1. The POI is 0. As x->infinity the limit -> -infinity and vice versa. Coordinates are (1,-2), (0,-6), (-1,-10). I've also graphed it to match my findings.

b) I'm not sure what to do for this part.

Part a) looks correct

For part b) you just need to find the equation of the tangent to the curve at that point. So you'll need the coordinate of y at x=2 and the gradient at x=2. {gradient function=$\frac{dy}{dx}$

 

[duki]

hmm... I'm getting like 2,-13 and 2,-75? Don't think I understand what you mean...

 

[Feldoh]

For part b) your just asked for the equation of a line that is tangent to the curve.

Well you need a point and a slope. They give you the point: it's when x=2. Finding y' gives you the slopes at every point (btw gradient is a fancy word for slope in this case), we need the slope at x=2 because that's the point that the line needs to be tangent.

 

[duki]

so like $$y = -75x + -28$$ ?

 

[Feldoh]

point slope form is:

$$y-y_0=m(x-x_0)$$

Where (x_0,y_0) is your point and m is your slope.

 

[Defennder]

You can use this online tool to check your answer:
http://fooplot.com/index.php?