5. Graphical Applications of Derivatives

Use the second derivative test to find the local extrema of the given function.

$g(x)=x^3-6x^2+9x+2$

Identify the inflection points and local maxima and minima of the functions graphed in Exercises 1–8. Identify the open intervals on which the functions are differentiable and the graphs are concave up and concave down.

8. y = 2cosx - √2x, -π≤x≤3π/2

Use the second derivative test to find the local extrema of the given function.

$f\left(x\right)=\frac{x^2-4}{x^2+1}$

Use the second derivative test to find the local extrema of the given function.

$f\left(x\right)=4\sin x\cos x$; $0$ < $x$ < $\pi$

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = 6x² - x³

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = x³ - (3/2)x² - 36x

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = eˣ(x - 2)²

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = 2x³ - 3x² + 12

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = x²e⁻ˣ

Second Derivative Test Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima.

f(x) = 2x² ln x - 11x²