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For the function f(x)=x^(2)+3, find the slope of the secant line between x=1 and x=3. Answer:

For the function f(x)=x2+3 f(x)=x^{2}+3 , find the slope of the secant line between x=1 x=1 and x=3 x=3 .\newlineAnswer:

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Q. For the function f(x)=x2+3 f(x)=x^{2}+3 , find the slope of the secant line between x=1 x=1 and x=3 x=3 .\newlineAnswer:
  1. Slope Formula: To find the slope of the secant line between two points on a function, we use the slope formula: slope=f(x2)−f(x1)x2−x1\text{slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}, where x1x_1 and x2x_2 are the x-coordinates of the two points.
  2. Calculate f(1)f(1): First, we need to calculate the value of the function at x=1x=1: f(1)=(1)2+3=1+3=4f(1) = (1)^2 + 3 = 1 + 3 = 4.
  3. Calculate f(3)f(3): Next, we calculate the value of the function at x=3x=3: f(3)=(3)2+3=9+3=12f(3) = (3)^2 + 3 = 9 + 3 = 12.
  4. Find Slope: Now, we can find the slope of the secant line using the values of f(1)f(1) and f(3)f(3): slope=f(3)−f(1)3−1=12−43−1=82=4\text{slope} = \frac{f(3) - f(1)}{3 - 1} = \frac{12 - 4}{3 - 1} = \frac{8}{2} = 4.

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