Question

(a)Use differentiation to find the minimum value of f(x)= 3x^2 - 5x + 10 and the value(s) of x for which this minimum occurs.

(b)Verify that this is a minimum

Answer 1

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.