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For the function f(x)=x^(2)-10, find the slope of the secant line between x=-1 and x=2. Answer:

For the function f(x)=x2−10 f(x)=x^{2}-10 , find the slope of the secant line between x=−1 x=-1 and x=2 x=2 .\newlineAnswer:

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Q. For the function f(x)=x2−10 f(x)=x^{2}-10 , find the slope of the secant line between x=−1 x=-1 and x=2 x=2 .\newlineAnswer:
  1. Calculate Function Values: To find the slope of the secant line between two points on a function, we use the formula for slope, which is (change in y)/(change in x)(\text{change in } y) / (\text{change in } x), or f(x2)−f(x1)x2−x1\frac{f(x_2) - f(x_1)}{x_2 - x_1}. We need to calculate the function values at x=−1x = -1 and x=2x = 2.
  2. Function Value at x=−1x = -1: First, we calculate the function value at x=−1x = -1.f(−1)=(−1)2−10=1−10=−9.f(-1) = (-1)^2 - 10 = 1 - 10 = -9.
  3. Function Value at x=2x = 2: Next, we calculate the function value at x=2x = 2.f(2)=(2)2−10=4−10=−6.f(2) = (2)^2 - 10 = 4 - 10 = -6.
  4. Find Two Points: Now we have the two points on the function: (−1,f(−1))=(−1,−9)(-1, f(-1)) = (-1, -9) and (2,f(2))=(2,−6)(2, f(2)) = (2, -6). We can use these to find the slope of the secant line.
  5. Calculate Slope: The slope of the secant line is (f(2)−f(−1))/(2−(−1))=(−6−(−9))/(2−(−1))=(3)/(3)=1(f(2) - f(-1)) / (2 - (-1)) = (-6 - (-9)) / (2 - (-1)) = (3) / (3) = 1.

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