Application of Derivatives Test

Result

Application of Derivatives Test - 67

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Question 1
1 / -0

At any point on the curve $$2x^{2}y^{2}-x^{4}=c$$, the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to

A
ordinate

B
radius vector

C
x-intercept of tangent

D
sub-tangent

Solution
Question 2
1 / -0

If f(x) and g(x) are differentiable function for $$0 \leq x\leq 1$$ such that f(0) = 10 , g(0) = 2, f(1) = 2, g(1) =4, then in the interval (0,1)

A
f (x) = 0 for all x

B
f (x) + 4g' (x) =0for at least one x

C
f (x) +2g' (x) for at most one x

D
none of these

Solution
Question 3
1 / -0

Given $$g(x)= \dfrac{x+2}{x-1}$$ and the line 3x + y -10 =0, then the line is

A
tangent to g(x)

B
normal to g(x)

C
chord of g(x)

D
none of these

Solution
Question 4
1 / -0

If the is an error of k% in measuring the edge of a cube, then the percent error in estimating its volume is

A
k

B
3k

C
$$\dfrac{k}{3}$$

D
None of these

Solution
Question 5
1 / -0

If the line joining the point (0, 3 ) and (5, -2) is a tangent to the curve $$y= \dfrac{c}{x+1}$$, then the value of c is

A
1

B
-2

C
4

D
None of these

Solution
Question 6
1 / -0

$$f(x) = \left\{\begin{matrix} -x^2, & \text{for} \ x < 0 \\ x^2 + 8, & \text{for} \ x \ge 0 \end{matrix}\right.$$
Let . Then x-intercept of the line, thet is , the tangent to the graph of f(x) is

A
zero

B
-1

C
-2

D
-4

Solution
Question 7
1 / -0

The equation of the curve $$y = be^{-x/a}$$ at the point where it crosses the y-axis is

A
$$\dfrac{x}{a}-\dfrac{y}{b}=1$$

B
$$ax = by = 1$$

C
$$ax-by=1$$

D
$$\dfrac{x}{a}+\dfrac{y}{b}=1$$

Solution
Question 8
1 / -0

A curve is represented by the equations $$x=sec^{2}t$$ and $$y=\cot t,$$ where t is a parameter. If the tangent at the point P on the curve, where $$t=\pi /4$$, meets the curve again at the point Q, then $$\left | PQ \right |$$ is equal to

A
$$\dfrac{5\sqrt{3}}{2}$$

B
$$\dfrac{5\sqrt{5}}{2}$$

C
$$\dfrac{2\sqrt{5}}{3}$$

D
$$\dfrac{3\sqrt{5}}{2}$$

Solution
Question 9
1 / -0

Let f be a continuous, differetiable and bijective function. If the tangent to y= f (x) at x = a is also the normal to y = f (x) at x = b then there exists at least one $$c \epsilon (a, b)$$ such that

A
f'(c) = 0

B
$$f (c)> 0$$

C
$$f (c)< 0$$

D
None of these

Solution
Question 10
1 / -0

Given the curves $$y=f(x)$$ passing through the point $$(0, 1)$$ and $$y=\displaystyle \int_{-\infty}^{x}{f(t)}$$ passing through the point $$\left( 0, \dfrac{1}{2}\right).$$ The tangents drawn to both the curves at the points with equal abscissae intersect on the $$x$$- axis. Then the curve $$y=f(x)$$ is

A
$$f(x)=x^2+x+1$$

B
$$f(x)=\dfrac{x^2}{e^x}$$

C
$$f(x)=e^{2x}$$

D
$$f(x)=x-e^x$$