Answer:
4
Step-by-step explanation:
f(x) = 1/2 *[tex]x^{2}[/tex] + 2x - 5
f'(x) = d/dx (1/2 * [tex]x^{2}[/tex] + 2x - 5)
=d/dx 1/2 *[tex]x^{2}[/tex] + d/dx 2x - d/dx 5
d/dx 1/2 * [tex]x^{2}[/tex] = x [Because to differentiate a exponential, you multiply the coefficient by the exponent (1/2 * 2) and then subtract 1 from the exponent: 2-1 = 1]
d/dx 2x = 2 [same as the explanation above]
d/dx 5 = 0 [differentiating a constant always equals zero]
so f'(x) = x+2
so f'(2) = 2+2 =4
