How to find local maximum graphing functions of curves

Practice Questions

CLEP Calculus › How to find local maximum graphing functions of curves

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1

What is the local maximum of ?

2

Consider the family of curves given by $f(x)=\frac{ax}{1+bx^2}$ with . If is a local maximum, determine and .

3

Determine the local maxima of the following function:

4

Find all the x values which have a local maxima of .

Graph to confirm your answer.

5

Determine the local maxima for the following function:

$\frac{x^3}{3}-(5+p)\frac{x^2}{2}+5px$

where p is a constant, $-\infty < p<5$ .

6

Which of the following are local maxima of the function $f(x)=e^{x}\sin(x)$ on the interval $[0,2\pi]$ ?

7

The postion of a feather in a windstorm is given by the following equation:

$x(t)= \frac{t^{3}}{3}+\frac{t^{2}}{2}-6t$

Determine when an extrema in the feather's position occurs and state whether it is a local minima or maxima.

8

Given a graph with equation , find the local maximum(s) in the graph if there are any.

9

Determine the local maxima of the function:

$f(x)=\frac{x^3}{3}-16x$

10

What is the local maximum of the following function in the interval ?

${} \text{f}(x) = x^3-12x^2+36x+1$

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