Chapter 10: Q. 1 (page 700)

For $f (x) = - 3 x^{2} + 5 x - 2, find \frac{f (x + h) - f (x)}{h}, h \neq 0$

Short Answer

Expert verified

The required answer is $- 6 x - 3 h + 5$

Step by step solution

Step 1. Given Information

The given function is $f (x) = - 3 x^{2} + 5 x - 2$

Step 2. Calculation

Substitute $x + h for x$ in the given function and expand the expression.

$f (x + h) = - 3 {(x + h)}^{2} + 5 (x + h) + 2 = - 3 (x^{2} + 2 x h + h^{2}) + 5 x + 5 h + 2 = - 3 x^{2} - 6 x h - 3 h^{2} + 5 x + 5 h + 2$

Substitute the values in the expression $\frac{f (x + h) - f (x)}{h}$ and simplify.

$\frac{f (x + h) - f (x)}{h} = \frac{(- 3 x^{2} - 6 x h - 3 h^{2} + 5 x + 5 h + 2) - (- 3 x^{2} + 5 x + 2)}{h} = \frac{- 6 x h - 3 h^{2} + 5 h}{h} = - 6 x - 3 h + 5$

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For $f (x) = - 3 x^{2} + 5 x - 2, find \frac{f (x + h) - f (x)}{h}, h \neq 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Forf(x)=-3x2+5x-2,findf(x+h)-f(x)h,h≠0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

For $f (x) = - 3 x^{2} + 5 x - 2, find \frac{f (x + h) - f (x)}{h}, h \neq 0$