Applications of Derivatives
Math ⇒ Calculus
Applications of Derivatives starts at 11 and continues till grade 12.
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See sample questions for grade 12
A ball is thrown vertically upward with a velocity of 20 m/s. The height at time t seconds is given by h(t) = 20t - 5t². Find the time when the ball reaches its maximum height.
A box with a square base and open top must have a volume of 32,000 cm³. Find the dimensions that minimize the amount of material used.
A particle moves along a line so that its position at time t is given by s(t) = t³ - 6t² + 9t. Find the time when the particle is at rest.
A rectangle has a perimeter of 20 units. What is the maximum possible area of the rectangle?
Find the equation of the tangent line to the curve y = x² at the point (1,1).
Find the intervals where the function f(x) = x² - 4x + 3 is increasing.
Find the local maxima and minima of the function f(x) = x³ - 6x² + 9x + 1.
Find the maximum value of the function f(x) = -x² + 4x + 5.
Given f(x) = x⁴ - 4x³, find the x-coordinates of the inflection points.
If f(x) = x³ - 3x² + 2, find the critical points of f(x).
If f(x) = x⁴ - 4x², find the intervals where the function is concave down.
If the derivative of a function is always positive, what can you say about the function?
If the tangent to the curve y = f(x) at x = a is horizontal, what is the value of f'(a)?
What is the derivative of a function used to determine about the function's graph?
