Question

Which of the two functions below has the largest maximum y-value?

f(x) = -x4- 2
g(x) = -3x3 + 2

Answer 1

g(x)=-3x^{3}+2

Explanation:

g(x) has a range that of (-infinity, +infinity), whereas f(x) has a range of (-infinity, -2].

Answer 2

Explanation:

● f(x) = -x^4 -2

● g(x) = -3x^3 + 2

Derivate both functions:

● f'(x) = -4x^3

● g'(x) = -9x^2

Solve the equations f'(x) =0 and g'(x) =0

● f'(x) = 0

● -4x^3 = 0

● x^3 = 0

● x =0

● g'(x) = 0

● -9x^2 = 0

● x^2 =0

● x = 0

So both functions f and g reach their maximum at 0.

● f(0) = 0^4-2 = -2

● g(0) = -3×0^3 +2 = 2

So g(0)>f(0)

So g has the largest maximum value.