The terminal side of an angle in standard position passes through the point (-2,-4). Use the figure to find the following value: tan⁡ θ

Hi! Your answer is 3x²

Please read an explanation for a clear understanding to the problem.

Any questions about the answer/explanation can be asked through comments! :)

Step-by-step explanation:

Goal

Find the limit of f(x+h)-f(x)/h when h --> 0

Given

A Cubic Function

Step 1

Rewrite the limit

Since f(x) = x³-9. Therefore, f(x+h) would be (x+h)³-9

Simplify the numerator

Step 2

Factor the numerator so we don't let h = 0.

When finding a limit of function, we can't let the approaching variable equal to 0 (Unless if a function doesn't really have limits.)

Cancel both h-term from denominator and numerator

Step 3

Substitute h = 0 in the expression.

Since we can't proceed anymore, therefore. The answer is 3x²

Additional Information

This is the limit method to find a derivative of function.To find a derivative for polynomial without using limit method, we can do by let exponent become a coefficient then subtract exponent by 1. For example, if you want to differentiate x³ the answer will be 3x².