Question

Determine whether f(x)=-4(x+3)^2-5 has a maximum or a minimum value, then find that value

Answer 1

Answer:

Yes it has

Step-by-step explanation:

From my perspective.........

f(x) = -4(x + 3)² - 5

f(x) = -4(x + 3)(x + 3) - 5

f(x) = -4(x² + 6x + 9) - 5

f(x) = -4x² - 24x - 36 - 5

f(x) = -4x² - 24x - 41

Dy/dx = -8x - 24

At minimum Dy/dx = 0

-8x - 24 = 0

-8x = 24

x = 24/-8

x = -3

At minimum

y = -4x² - 24x - 41

y = -4(-3)² - 24(-3) - 41

y = -4(9) + 72 - 41

y = -36 + 72 - 41

y = 36 - 41

y = -5