Question

For the Function f(x)=2X^3-7x^2+4x+1

a) find the instantaneous rate of change at x=0 and x=1

b)Is the function increasing or decreasing at x=0? x=1?

c)Do you expect a local min or max when 0 12 years ago

Answer 1

f'(x) = 6x^2 - 14x + 4
f'(1) = 6(1)^2 - 14(1) + 4
f'(1) = 6 - 14 + 4
f'(1) = -4
f'(0) = 6(0)^2 - 14(0) + 4
f'(0) = 4
since the instantaneous rate of change (read: derivative) at x = 0 is positive, the function is increasing at x = 0
since the instantaneous rate of change (read: derivative) at x = 1 is negative, the function is decreasing at x = 1
since from left to right (the graph of x = 0 to x = 1), the function switches from increasing to decreasing, it looks like there would be a maximum between 0 and 1

Answer 2

Refer to the attached Mathematica solution.