Find the maximum rate of increase of the function y = -x^3 + 6x^2 - 5x + 3.
Answer and explanation
Correct answer: C. 7
- Step 1: Rate of increase is the derivative: y' = -3x^2 + 12x - 5. Step 2. To maximize y', find where its derivative is zero: y'' = -6x + 12 = 0 => x = 2. Step 3. Since y''' = -6 < 0, x = 2 gives the maximum of y'. Step 4. Evaluate y' at x = 2: y'(2) = -3(4) + 12(2) - 5 = -12 + 24 - 5 = 7. Answer: 7. Why not the others: 5 is the constant in y'; 6 is the coefficient of x^2; 8 is an addition slip.
Practise more Probability, Statistics, Combinatorics and Calculus Fundamentals.
Free questions with an explanation for every one, and full timed Nationella prov (Sweden) mock tests.
More Probability, Statistics, Combinatorics and Calculus Fundamentals questions
- Evaluate the derivative of the function f(x) = 4x^3 - 5x^2 + 7x - 9 with respect to x.
- Find the equation of the tangent line to the curve f(x) = x^2 - 4x + 6 at the point where x = 3.
- How many distinct 4-person committees can be formed from a group of 9 eligible candidates?
- A bag contains 5 red balls, 4 blue balls, and 3 green balls. Two balls are drawn without replacement. What is the probability that both ball…
- Find all critical points of the function g(x) = 2x^3 - 9x^2 + 12x + 1.
- A discrete dataset has values: 4, 7, 7, 8, 9, 10, 11, 14. What is the interquartile range (IQR) of this data?