How do you find slopes at specific points with tangent functions??

Step-by-step explanation:

The slope of the tangent line of a function f(x) is the derivative, f'(x).

Here, we can use exponent rule to find the derivatives:

If y = xⁿ, then y' = nxⁿ⁻¹.

7. g(x) = x²

g'(x) = 2x

g'(2) = 4

8. g(x) = x² − 4x

g'(x) = 2x − 4

g'(1) = -2

9. g(x) = 5/(x + 3)

g(x) = 5 (x + 3)⁻¹

g'(x) = -5 (x + 3)⁻²

g'(-2) = -5

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3