7. For a given function y = F(x), say that we know the following information: F(-1)...

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7. For a given function y = F(x), say that we know the following information: F(-1) = -5 and F'(x) is given by the formula F'(x) = 1-}x¹. Again, the formula given is F'(x), the derivative of F(x). Throughout the following questions, proper and correct notation is essential. (a) Find a formula for L(x), the tangent line approximation to y = F(x), at the point (a, F(a)), where a = -1. (b) Use the tangent line approximation you found in (a) to estimate F(-0.92). Clearly show your work using proper notation. (c) Is the estimate you found in (b) too large or too small? Why? 8. Consider the two piecewise linear functions p and q given by the figure below. Determine each of the following derivative values that involve functions that are defined in terms of r and Clearly show your work and thinking using proper notation, be sure your values are exact in light of the giv information, and write one sentence to explain your overall approach. (a) Let R(x) = 6-2g(x). Find R'(-2). (b) Let S(x) = p(x) + g(x). Find S(-0.5). (c) Let T(x) = 79(x)-3p(x). Find 7(1). 7. For a given function y = F(x), say that we know the following information: F(-1) = -5 and F'(x) is given by the formula F'(x) = 1-}x¹. Again, the formula given is F'(x), the derivative of F(x). Throughout the following questions, proper and correct notation is essential. (a) Find a formula for L(x), the tangent line approximation to y = F(x), at the point (a, F(a)), where a = -1. (b) Use the tangent line approximation you found in (a) to estimate F(-0.92). Clearly show your work using proper notation. (c) Is the estimate you found in (b) too large or too small? Why? 8. Consider the two piecewise linear functions p and q given by the figure below. Determine each of the following derivative values that involve functions that are defined in terms of r and Clearly show your work and thinking using proper notation, be sure your values are exact in light of the giv information, and write one sentence to explain your overall approach. (a) Let R(x) = 6-2g(x). Find R'(-2). (b) Let S(x) = p(x) + g(x). Find S(-0.5). (c) Let T(x) = 79(x)-3p(x). Find 7(1).