- #1
f22archrer
- 14
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Homework Statement
f(x) = (-5x^2+3x) / (2x^2-5)
Homework Equations
f 'x)=
(-6x^2+50x-15) / ( 2x^2-5)^2
The Attempt at a Solution
f ''x= ?
f22archrer said:Homework Statement
f(x) = (-5x^2+3x) / (2x^2-5)
Homework Equations
f 'x)=
(-6x^2+50x-15) / ( 2x^2-5)^2
The Attempt at a Solution
f ''x= ?
f22archrer said:f'(x) = (2x^2 -5)((-10x+3) -(-5x^2+3x)4x) / 2x^2-5
= -20x^3 +6x^2+50x-15+20x^3-12x^2 / (2x^ - 5)^2
= -6x^2 +50x-15 / (2x^2 - 5)^2
It helps to use sufficient number of parentheses. A little spacing can also help.f22archrer said:f'(x) = ((2x^2 -5)( -10x+3) -(-5x^2+3x)4x) / (2x^2-5) 2
= (-20x^3 +6x^2+50x-15+20x^3-12x^2 ) / (2x^ - 5)^2
= ( -6x^2 +50x-15 ) / (2x^2 - 5)^2
The double derivative is the derivative of the derivative of a function. It represents the rate of change of the slope of a function, or the curvature of the graph at a specific point.
The double derivative can be found by taking the derivative of the first derivative of a function. This can be done using the power rule, product rule, quotient rule, or chain rule depending on the function.
The notation for the double derivative is f''(x) or d2y/dx2.
The double derivative is important because it helps us understand the behavior of a function. It can tell us if a function is increasing or decreasing, concave up or concave down, and if it has any points of inflection.
Yes, the double derivative can be negative. This indicates that the function is concave down at a specific point, and the slope of the function is decreasing.