Suppose that y = f(z) is a differentiable function for which the following information is known: (2) =15, F(2) = =1, '{2)= 0:26; Answer the following questions. (a) Is f increasing or decreasing at = 2? O increasing O decreasing (b) Is f concave up or concave down at x = 2? O concave up O concave down (c) Do you expect f(2.1) to be greater than 1.5, equal to 1.5, or less than 1.5? O greater than 1.5 Oequal to 1.5 O less than 1.5 (e) Do you expect f'(2.1) to be greater than 1, equal to 1, or less than 1? O greater than 1 O equal to 1 O less than 1 Suppose that f is a function given as f(x) = 3x2 + 5x. Simplify the expression f(x + h). f (act h) = Simplify the difference quotient, f(ath) - f(2) h f(ath) - f(2) h The derivative of the function at x is the limit of the difference quotient as h approaches zero. f'(ac) =lim f(ath) - f(2) = h-+0 hSuppose that f is a function given as f(z) = . We will compute the derivative of f at x = 7 as -3z -2 follows. First, we compute and simplify the expression f(7 + h). f(7T+h) = Then we compute and simplify the difference quotient, between z = 7and z = 7 + h. A h The derivative of the function at z is the limit of the difference quotient as h approaches zero. , . f(T+h) f(7) p =g 2O Match each function with its graph Function Graph Color E f'(z) a. red (av] f(z) b. blue E] f'(z) c. green The slope of the tangent line to the parabola y = 4% + 7z + 5 at the point (4, 97) is: The equation of this tangent line can be written in the form y = ma + b where m is: Find the derivative of: 6~ %* Use e\"x for e\". -] Now, find the equation of the tangent line to the curve at z = 0. Write your answer in mx + b format. cos(5x). [Hint: use product rule and chain rule!] \f\f\fThe function f(z) = 9z + 6z~ has one local minimum and one local maximum. Algebraically use the derivative to answer the questions: (Leave answers in 4 decimal places when appropriate) this function has a local maximum at = Consider the function f(x) = x - 72x2 + 3, - 5