Ünite Sınavı Soruları

What is the derivative of the function which is given below?

f(x)=3x.e^-5x

Find the interval of decrease for the function .

For the function , find the derivative function f'(x)?

Three sides of a rectangular enclosure having one side along a wall must be fenced. Assume that 500 m of fence is available. Find the largest possible area of the enclosure.

A particle moves along the x-axis in such a way that its position at time t is . Find the average velocity over the interval [1, 4].

What is the first derivative of the function f(x)=(2/x)+3x²

Given the function , find the derivative at the point x=0.

At which point on the graph of the function the slope is zero?

What is the derivative of the function f(x)=(x³-7) / (3x²+1) at the point x=1?

Which of the following is the slope of the graph of  at the point (0, 0)?

Which of the following gives the instantaneous velocity of a particle at time t if its' position at time t is defined by f(t)?

The motion of a particle is given by the function f(t) = 2t² – t  Find its velocity at the instant t = 3.

Which of the following functions is monotone increasing in interval (-∞, +∞) | x ≠0?

A car moves along a road in such a way that its position at time t is f(t) = t³ + t² + t (metre). What is the velocity of the car at the instant t=2 equal to?

Which of the following gives the average velocity of a particle in time interval (t₁, t₂) if its' position at time t is defined by f(t)?

For the function f(x)=-3x+11, find the derivative f'(x) at the point x=0?

If f(x) is differentiable on an interval I,

I.  f '(x) < 0 for all x ∈ (a, b) then f(x) is called monotone increasing

II. f '(x) > 0 is satisfied for all x ∈ (a, b) then f(x) is called monotone increasing

III. f '(x) > 0 is satisfied for all x ∈ (a, b) then f(x) is called monotone decreasing

IV. f '(x) < 0 for all x ∈ (a, b) then f(x) is called monotone decreasing

which of the given statements is true about monotonicity?

At which point on the graph of the function the slope is zero?

For the given f(x) =2x² + 2x + 2 function which of the statements are true?