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I have a multiple part problem in my Calculus book I'm trying to figure out while I practice for a test. The given function is $F(x)= -2x^3 + 6x^2 - 3x$, and I have the following parts solved:

a. Find $F'(x) = -6x^2 + 12x - 3$

b. Find $F''(x) = -12x + 12$

Can someone walk me through how to go about the following?

Find the intervals on which the function is:

c. Increasing

d. Decreasing by using the 1st Derivative Test.

Find the intervals on which the function is:

e. Concave Up

f. Concave Down using the 2nd Derivative Test.

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1 Answer 1

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c,d) the interval which the function is increasing is when $F'(x) > 0$, you find this by equating $F'(x) = 0$ where you will find 2 $x$ values, you will have to plot the function to see where $F'(x) > 0$ or $F'(x) < 0$, then simply write down where $F'(x) > 0$ since you found places where you function cuts the y axes . T.L.D.R find where $F'(x) > 0$ or $F'(x) < 0$.

e,f) you functions is conceiving up when $F''(x) > 0$ an vice versa, equate $F''(x) = 0$ and you will find one $x$ value plot the function to see where $F''(x) > 0$ and write down where $F''(x) > 0$ and vice versa

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