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For the function f(x)=10x^(2)+7x-6, find the slope of the tangent line at x=-4. Answer:

For the function f(x)=10x2+7x−6 f(x)=10 x^{2}+7 x-6 , find the slope of the tangent line at x=−4 x=-4 .\newlineAnswer:

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Q. For the function f(x)=10x2+7x−6 f(x)=10 x^{2}+7 x-6 , find the slope of the tangent line at x=−4 x=-4 .\newlineAnswer:
  1. Calculate Derivative: To find the slope of the tangent line at a specific point, we need to calculate the derivative of the function, which gives us the slope of the tangent line at any point xx.
  2. Find Derivative Function: The derivative of f(x)=10x2+7x−6f(x) = 10x^2 + 7x - 6 with respect to xx is f′(x)=20x+7f'(x) = 20x + 7.
  3. Evaluate at x=−4x = -4: Now we need to evaluate the derivative at x=−4x = -4 to find the slope of the tangent line at that point.
  4. Substitute x=−4x = -4: Substitute x=−4x = -4 into the derivative to get f′(−4)=20(−4)+7f'(-4) = 20(-4) + 7.
  5. Calculate f′(−4)f'(-4): Calculate the value of f′(−4)f'(-4) which is f′(−4)=−80+7f'(-4) = -80 + 7.
  6. Simplify and Final Value: Simplify the expression to get the final value of the slope at x=−4x = -4, which is f′(−4)=−73f'(-4) = -73.

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