Math 110 Course Resources Curve Sketching Course Packet on critical points Consider the function f(x) = 4x~ + 3 x2 - 9 Enter the number of critical pointsumbers of f(x). 3 X Determine the x-coordinates of the critical points. Enter your answer as a comma separated list of values. The order of the values does not matter. Enter DNE if f(x) does not have any critical points. (-3,0,3) X(a) Consider the function f(x) = V x2 - 49. Enter the number of critical pointsumbers of f(x). 2 V Determine the x-coordinates of the critical points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if f(x) does not have any critical points. (-7,7) X (b) Consider the function g(x) = v 49 - x2. Enter the number of critical pointsumbers of g(x). 3 Determine the x-coordinates of the critical points. Enter your answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if g(x) does not have any critical points. (-7,0,7) XMath 110 Course Resources - Curve Sketching Course Packet on critical points Curve Sketching Course Packet on classifying critical points using the first derivative test The following graph corresponds to f'(x), the first derivative of f(x). If the graph does not appear, please reload the page. 1000 2000 -5 5 -2000 -4000 Based on the above graph of the derivative of f(x), determine the number critical points and relative extrema of f(x). You may assume that f'(x) is continuous, f'(x) is defined for all x, and f'(x) = 0 only when x = -7, x = 0, and x = 5. Enter the number of critical pointsumbers of f(x): 3 Enter the number of relative maxima of f(x) : 1 X Enter the number of relative minima of f(x): 2 XDetermine the x-coordinates of the relative extrema of the function g(x) = x4 - 12x3 - 104x2 - 8. Enter each answer as a comma-separated list of values. The order of the values does not matter. Enter DNE if g(x) does not have any relative maximum or minimum values, respectively. x-coordinates of the relative maxima = DNE X x-coordinates of the relative minima = (-4,13) X