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Choose the most appropriate option (a) (b) (c) or (d)
The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 is
- a)–12
- b)12
- c)0
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
ANSWER :- a
Solution :- 2x^3 - 3x^2 -12x + 8 = 0
dy/dx = 6x^2 - 6x -12 = 0
(At x=0) = 6(0)^2 - 6(0) - 12
= -12
Most Upvoted Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
Finding the Gradient of a Curve
- The gradient of a curve at a particular point is the slope of the tangent to the curve at that point.
- To find the gradient of a curve at a point, we need to differentiate the equation of the curve with respect to x, and then substitute the value of x at the point of interest.
Given Curve and Point
- The given curve is y = 2x^3 - 3x^2 - 12x + 8.
- The point of interest is x = 0.
Differentiating the Curve
- To find the gradient at x = 0, we need to differentiate the curve with respect to x.
- The derivative of y = 2x^3 - 3x^2 - 12x + 8 is:
dy/dx = 6x^2 - 6x - 12
Substituting x = 0
- Now we need to substitute x = 0 in the derivative to find the gradient at x = 0.
- When we substitute x = 0 in the derivative, we get:
dy/dx = 6(0)^2 - 6(0) - 12 = -12
- Therefore, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.
Answer
- The correct option is not given in the question, but option (a) 12 is incorrect.
- The correct answer is option (d) none of these, as the gradient at x = 0 is -12 and not 12.
- The gradient of a curve at a particular point is the slope of the tangent to the curve at that point.
- To find the gradient of a curve at a point, we need to differentiate the equation of the curve with respect to x, and then substitute the value of x at the point of interest.
Given Curve and Point
- The given curve is y = 2x^3 - 3x^2 - 12x + 8.
- The point of interest is x = 0.
Differentiating the Curve
- To find the gradient at x = 0, we need to differentiate the curve with respect to x.
- The derivative of y = 2x^3 - 3x^2 - 12x + 8 is:
dy/dx = 6x^2 - 6x - 12
Substituting x = 0
- Now we need to substitute x = 0 in the derivative to find the gradient at x = 0.
- When we substitute x = 0 in the derivative, we get:
dy/dx = 6(0)^2 - 6(0) - 12 = -12
- Therefore, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.
Answer
- The correct option is not given in the question, but option (a) 12 is incorrect.
- The correct answer is option (d) none of these, as the gradient at x = 0 is -12 and not 12.
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Community Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
Diff w.r.t.x
dy/dx = 2 d/dx x^3 - 3 d/dx x^2 - 12 d/dx x + d/dx 8
= 6x^2-6x-12
put x=0
=6*0-6*0-12
= -12
dy/dx = 2 d/dx x^3 - 3 d/dx x^2 - 12 d/dx x + d/dx 8
= 6x^2-6x-12
put x=0
=6*0-6*0-12
= -12
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