Solving and sketching the graph of a polynomial function using Mathematical Software (Maple Software) 1 2 3 4 Define the function f(x) = 4x - 24x+36x Find the i) x-intercept ii) y-intercept Find the critical points using the following

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Solving and sketching the graph of a polynomial function using Mathematical Software (Maple Software) 1 2 3 4 Define the function f(x) = 4x³ - 24x²+36x Find the i) x-intercept ii) y-intercept Find the critical points using the following steps: i) Differentiate f ii) Factorize" iii) Solve f' = 0 (determine x₁ and X₂ iv) Find f(x₁) v) Find f(x₂) Find the interval(s) where f is increasing or decreasing using the following steps: i) ii) Find the first derivative and denote it by Determine the interval(s) on which is increasing (f(x) > 0) or decreasing (f(x) <0) by substituting a test value from each interval. State the points for i) x-intercept ii) y-intercept What are the critical points? On which interval is increasing On which interval is decreasing 5 6 7 Determine the extrema using the Second Derivative test by carrying out the following steps: i) Find the second derivative of f(f(x)) and denoted it by DRI ii) Find f'(x₁) and f'(x₂) to determine if f'(x) > 0 or <0 ƒ' (x₂)> 0 or <0 iii) Evaluate f(x) to find the extrema. Determine the inflection point Solve f'(x)=0 Find the interval(s) of concavity. Concave up (f'(x) > 0) and concave down (f(x) < 0) by substituting a test value from each interval. i) ii) Sketch the graph off by drawing a curve that passes through the critical points and the inflection point. Label the critical points, the inflection point, minimum and maximum point. Minimum point: Maximum point: On which interval isf concave up On which interval is ✓ concave down State the inflection point

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