Applications of Derivatives

Math ⇒ Calculus

Applications of Derivatives starts at 11 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Applications of Derivatives. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

A ball is thrown upwards and its height at time t seconds is given by h(t) = -5t² + 20t + 2. Find the time when the ball reaches its maximum height.

A box with a square base and open top must have a volume of 32 cubic units. What is the minimum surface area?

A function has a critical point at x = 2. If f''(2) = 0, what can you conclude about the nature of the critical point?

A rectangle has a perimeter of 20 units. What is the maximum possible area of the rectangle?

Find the critical points of the function f(x) = x³ - 3x² + 2.

Find the equation of the normal line to the curve y = x² at x = 1.

Find the equation of the tangent line to the curve y = x³ at x = 1.

Find the inflection point(s) of the function f(x) = x³ - 6x² + 12x - 5.

Find the local maximum and minimum values of f(x) = x² - 4x + 3.

Find the maximum value of f(x) = -x² + 4x + 1.

Find the maximum value of the function f(x) = 2x - x² on the interval [0, 3].

Find the minimum value of the function f(x) = x² + 6x + 10.

Given f(x) = 2x⁴ - 8x², determine the intervals where the function is decreasing.

If f(x) = x² - 2x + 1, what is the minimum value of f(x)?

If f(x) = x² + 3x + 2, find the value of f'(2).

If f(x) = x³ - 3x, find the intervals where the function is concave up.

If f(x) = x⁴ - 4x³ + 6x², find all points of inflection.

If f'(x) changes from positive to negative at x = c, what does this indicate about f(x) at x = c?

If the position of a particle is given by s(t) = t³ - 6t² + 9t, find the time when the particle changes direction.

If the second derivative of a function at x = a is positive, what does this indicate about the function at x = a?