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If y = 5x2 + 3, then the tangent at x = 0, y = 3
- a)passes through x = 0, y = 0
- b)has a slope of +1
- c)is parallel to the x-axis
- d)has a slope of -1
Correct answer is option 'C'. Can you explain this answer?
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If y = 5x2 + 3, then the tangent at x = 0, y = 3a)passes through x = 0...
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If y = 5x2 + 3, then the tangent at x = 0, y = 3a)passes through x = 0...
Given equation: y = 5x^2 - 3
To find the tangent at x = 0, y = 3, we need to find the slope of the tangent.
Step 1: Find the derivative of the equation y = 5x^2 - 3
The derivative of y with respect to x gives us the slope of the tangent at any point on the curve.
dy/dx = d/dx (5x^2 - 3)
= 10x
Step 2: Substitute x = 0 into the derivative
To find the slope of the tangent at x = 0, we substitute x = 0 into the derivative obtained in step 1.
dy/dx = 10(0)
= 0
Step 3: Interpret the slope of the tangent
The slope of the tangent at x = 0 is 0. A slope of 0 indicates that the tangent is parallel to the x-axis.
Therefore, the correct answer is option C: The tangent is parallel to the x-axis.
Explanation:
The slope of a tangent line represents the rate of change of the function at a specific point. In this case, since the slope is 0, it means that the function does not change as x varies. This implies that the tangent line is parallel to the x-axis.
Visually, if we plot the function y = 5x^2 - 3, we will see that it is a parabola opening upwards. At x = 0, y = 3, the point lies on the curve. The tangent at this point will be a horizontal line, which is parallel to the x-axis.
Hence, option C is the correct answer.
To find the tangent at x = 0, y = 3, we need to find the slope of the tangent.
Step 1: Find the derivative of the equation y = 5x^2 - 3
The derivative of y with respect to x gives us the slope of the tangent at any point on the curve.
dy/dx = d/dx (5x^2 - 3)
= 10x
Step 2: Substitute x = 0 into the derivative
To find the slope of the tangent at x = 0, we substitute x = 0 into the derivative obtained in step 1.
dy/dx = 10(0)
= 0
Step 3: Interpret the slope of the tangent
The slope of the tangent at x = 0 is 0. A slope of 0 indicates that the tangent is parallel to the x-axis.
Therefore, the correct answer is option C: The tangent is parallel to the x-axis.
Explanation:
The slope of a tangent line represents the rate of change of the function at a specific point. In this case, since the slope is 0, it means that the function does not change as x varies. This implies that the tangent line is parallel to the x-axis.
Visually, if we plot the function y = 5x^2 - 3, we will see that it is a parabola opening upwards. At x = 0, y = 3, the point lies on the curve. The tangent at this point will be a horizontal line, which is parallel to the x-axis.
Hence, option C is the correct answer.
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If y = 5x2 + 3, then the tangent at x = 0, y = 3a)passes through x = 0, y = 0b)has a slope of +1c)is parallel to the x-axisd)has a slope of -1Correct answer is option 'C'. Can you explain this answer?
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