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Q1. The derivative of x³-4 at x=2 is:

• 8
• 12
• 16
• – 8

Solution

Q2. If the derivative of a function is small , the curve corresponding to the function is.

• More Steep
• More flat
• A straight line
• Has a break

Solution

Q3. The derivative of the constant function f(x)=a for a fixed real number ‘a’ is:

• 0
• 1
• a
• <br1/a

Solution

Q4. Consider the function f(x) = x + 10. Let us compute the value of the function f(x) for x very near to 5. Some of the points near and to the left of 5 and right to the 5 are given in the table. x 4.9 4.95 4.99 4.995 5.001 5.01 5.105 f(x) 14.9 14.95 14.99 14.995 15.001 15.01 15.105

• 10.5
• 15
• 14.9995
• 15.0005

Solution

From the Table, we deduce that value of f(x) at x = 5 should be greater than 14.995 and less than 15.001. It is reasonable to assume that the value of the f(x) at x = 5 as dictated by the numbers to the left of 5 is 15, i.e. Similarly, when x approaches 5 from the right, f(x) should be taking value 15, i.e., Thus,

Q5. Derivative of sum of two functions is sum of the derivatives of the functions. If , f and g be two functions such that their derivatives are defined in ______.

• Common domain
• Their individual domains
• Universally
• None of the above

Solution

Derivative of sum of two functions is sum of the derivatives of the functions.If , f and g be two functions such that their derivatives are defined in the common domain.

Q6. For the limit of a function to exist we must have

• LHL > RHL
• LHL <  RHL
• LHL = RHL
• LHL = 2 RHL

Solution

The limit of any function f(x) as x tends to a is possible when,  both left hand limit and right hand limit are equal.

Q7. The derivative of the function f(x)=2x²+3x-3 at x = – 2 is: 

• – 5
• 10
• 5
• – 10

Solution

Q8. The geometrical representation of derivative is linked to

• Perpendicularity of two lines.
• Parallelism of two lines
• Slope of a tangent to the given curve.
• Slope of any line intersecting   the curve at 90 degrees

Solution

The geometrical representation of derivative of a curve at a point is the slope of the tangent drawn to the curve at that point.

Q9. Derivative of sum of two functions is …… of the derivatives of the functions.

• Sum
• Difference
• Product
• Division

Solution

Q10. The derivative of x + a is.

• zero
• a
• 1
• -a

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