Question

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7

(a)Find the intervals on which f is increasing/decreasing and identify any local extrema.

(b) Find the intervals on which f is concave up/down and find any inflection points.

B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

Answer 1

Solution:-

A)

a) Differntiating with respect to x

.

For increasing interval

For decreasing interva

Local extrema at

b)

Differentiantin with respect to x

for concave up

interval

concave down

inflection point

b)

Differentiating with respect to x

Again differentiating with respect to x

at

at

maxima occurs at

minima occurs at