Pre Calc Introduction to Derivatives-Using Limits Help!

Attachment 1 : Option A,

Attachment 2 : Option D,

Attachment 3 : Option B,

Attachment 4 : Instantaneous rate of change will be 24

Step-by-step explanation:

"Remember that we can solve such questions by finding the derivative first"

1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.

The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.

2 : f'(5) = - 2 * 5 + 4,

f'(5) = - 10 + 4 = - 6

Your solution is option d.

3 : f'(2) = 12 / 2 + 1 / - 3,

f'(2) = 12 / 3 / - 3 = 4 / - 3,

f'(2) = - 4 / 3

Your solution is option b.

4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of  g .

g'(t) = 3(2x¹) + 0 = 6t,

And now we can evaluate the derivative at that value of  t.

g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24