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Question is in the picture, trying to find the slope.

Question is in the picture, trying to find the slope.-example-1
User Damir
by
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1 Answer

2 votes

Answer:

108

Explanation:

So the slope of the tangent line to the graph of y=4x² is:


\lim_(x \to 3) (4x^3-108)/(x-3)

As directed, try values near 3 to estimate the slope. So, using a calculator, I'm going to try 2.9, 2.99, and 2.999:

2.9:


(4(2.9)^3-108)/((2.9)-3)\approx104.44

2.99:


(4(2.99)^3-108)/((2.99)-3)\approx107.6404

2.999:


(4(2.999)^3-108)/((2.999)-3)\approx107.96

And let's also try 2.9999 and 2.99999. So:


(4(2.9999)^3-108)/((2.9999)-3)\approx107.9964

And:


(4(2.9999)^3-108)/((2.9999)-3)\approx107.99964

Let's also check by coming from the right with 3.001:


(4(3.001)^3-108)/((3.001)-3)\approx108.036

Therefore, our limit or slope is:


\lim_(x \to 3) (4x^3-108)/(x-3)\approx108

And we're done!

The answer is 108

User Ajinzrathod
by
7.4k points

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