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For the following function, use the given set of intervals to estimate the slope of the tangent line of the function at x=−2 by producing the slopes of the secant lines that pass through the x-values of each of the intervals. f(x)=2x 2 +1; [−4,−2],[−3,−2],[−2.5,−2],[−2.25−2]

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The slope of the tangent line of the function at x=-2 is; -8.

Slope of a line tangent to a curve

The slope of the line tangent to the given function; f(x) can be determined from the line f'(x) as follows;

  • f'(x) = 4x.

The slope of the tangent lines in each case can then be evaluated as follows;

Hence, the slope of the tangent line of the function, f(x) = 2x² +1 can then be evaluated by substituting, x=-2 into f'(x) as follows;

  • Slope = f'(-2) = 4(-2) ,= -8.

Read more on the slope of tangent to a functions;

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