Consider the function y=g(x)=-x^2+5x+2 (a) Use the limit definition to compute a formula for y=g'(x) y= (b) Determine the slope of the tangent line to y=g(x) at the value x=2 slope= (c) Compute g(2) g(2)= (d) The equation for the tangent line to y=g(x) at the point (2,g(2)) written in point-slope form, is y-square =square (x-square ) Fill in the blanks with the appropriate numbers.

(a) To compute the derivative of the function using the limit definition, we need to find the limit of the difference quotient as the change in approaches 0.The difference quotient is given by: Substituting the function into the difference quotient, we get: Taking the limit as approaches 0, we get: Therefore, the formula for the derivative is: (b) To determine the slope of the tangent line to at the value , we need to evaluate the derivative at .Substituting into the derivative formula, we get: Therefore, the slope of the tangent line to at the value is 1.(c) To compute , we need to substitute into the original function .Substituting , we get: Therefore, .(d) The equation for the tangent line to at the point written in point-slope form is: Substituting the values of and , we get: Therefore, the equation for the tangent line to at the point written in point-slope form is: