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Use the four step process to find the slope of the tangent line to the graph of the given...

Question:

Use the four step process to find the slope of the tangent line to the graph of the given function at any point. {eq}f(x)=10x^2 + 3x {/eq}

step 1: {eq}f(x+h)=? {/eq}

step 2: {eq}f(x+h)-f(x)=? {/eq}

step 3: {eq}\frac{f(x+h)-f(x)}{h}=? {/eq}

step 4: {eq}\displaystyle \lim_{h \to 0}\frac{f(x+h)-f(x)}{h}=? {/eq}

The slope of a curve:

If there is a function or curve which is represented by y = {eq}f\left(x\right) {/eq}, then the slope of the tangent to that curve can be calculated by differentiating that function with respect to its variable. The slope is represented by {eq}m {/eq} which is calculated by the formula {eq}\frac{\mathrm{d} y}{\mathrm{d} x} {/eq} or {eq}f^{'}\left(x \right ) {/eq}

Answer and Explanation: 1

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Given data

  • {eq}f_{x} {/eq} ={eq}10 x^{2}+3x {/eq}

Now use the four-step method to calculate the slope of the curve.

Step 1:

{eq}f( x+h) = 10...

See full answer below.


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Differentiation Strategy: Definition & Examples

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Chapter 7 / Lesson 15
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In this lesson, we'll learn about differentiation strategy. We'll define it and look at important characteristics. The lesson will then discuss the pros and cons of differentiation strategy.


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