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Find the relative changes for the function f(x) = x2 + 6x − 10 at x=1.

Mathematics

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Graph of f(x) = x² + 6x − 10

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Key points of f(x) = x² + 6x − 10
Pointxy
x-intercept−7.360
Minimum−3−19
y-intercept0−10
x-intercept1.360

Here are the relative changes for each function:

a) For f(x)=x2+6x−10f(x) = x^2 + 6x - 10:

Step 1: Find the derivative of f(x)f(x).

f′(x)=ddx(x2+6x−10)=2x+6f'(x) = \frac{d}{dx}(x^2 + 6x - 10) = 2x + 6

Step 2: Evaluate f(x)f(x) and f′(x)f'(x) at x=1x=1.

f(1)=(1)2+6(1)−10=1+6−10=−3f(1) = (1)^2 + 6(1) - 10 = 1 + 6 - 10 = -3
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