Question

Please show all calulations for each sub-question. Thank you

1. Assess the following functions (15 points):

1. 𝑓 ′(𝑥) = 𝑥 2 + 6𝑥 + 2

2. 𝑓 ′(𝑥) = 10𝑥 − 2𝑥 2 + 5 

a. Find the stationary points.

b. Determine whether the stationary point is a maximum or minimum.

c. Draw the corresponding curves, they can be in the same graph.

Answer 1

1.

$f'=2x+6,$

$f'=0,$

$x=-3$ (min),

$f(-3)=-7,$

2.

$f'=10-4x,$

$f'=0,$

$x=2.5$ (max),

$f(2.5)=17.5.$