Knowledge and Understanding continued... 6. Consider the function f (x) = x3 (1 mark for each part, 5 marks total) a) Estimate the slope of the tangent at x =() using the following values of h . i) h =1 ii) h =0.1 1) h =0.01 iv) h = 0.001 Therefore, lim f (0 +h) - f(0) b) Based on the results from above, what can you conclude about the tangent at x = 0? mark for Communication section)7. Distinguish between Average Rate of Change and Instantaneous Rate of Change, use an appropriate example to support your answer. (3 Marks) 8. The graph of function f (x) is shown below: (10 marks) a) For what value(s) of x is f (x) undefined? (1 mark) b) What type of discontinuity exists at x = -2? (1 mark)8. The graph of function f(x) is shown below: (10 marks) a) For what value(s) of x is f (x) undefined? (1 mark) b) What type of discontinuity exists at x = -2? (1 mark) c) At what value(s) of x is the function non-differentiable? (3 marks) d) Evaluate each limit: i) lim_f(x) ii) lim f (x) iii) lim f (x) iv) lim f(x) v) lim f(x)79% The graph below represents the average height of female children from birth to age 16. Height Chart for Females Height (cm) 9 10 19 12 18 Age (Years) a) Determine the average rate of change of height from age 0 to 3. b) Estimate the instantaneous rate of change of height at age 10.c) The graph above (question 1) can be modeled with the equation h(/) = -115(0.85) +165 where / is the height in cm, and / is the age in years Use the equation to verify the results from above: i) average ROC from age 0 to 3 ii) instantaneous rate of change of height at age 10. 10. Consider the following graph of function f(x): Evaluate: (3 marks) a) lim f (x)10. Consider the following graph of function f(x) : Evaluate: (3 marks) a) lim f(x) b) f (6) c) lim f (x) d) lim f(x) e) lim f(x) f) lim f(x)12. Find the equation of the tangent to the following functions at the indicated point. a) f(x) =2x - 3x+1 at x = 2 b) / (x) = x+7 at x =-1 2x - 1