Applications Of Derivatives – Tangents and Normal — Practice Quiz
Telangana Open School (TOSS) · Class 12 · Mathematics
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What is the slope of the tangent to the curve \( y = x^2 \) at \( x = 1 \)?
Find the slope of the tangent to \( y = 3x^2 - 2x + 1 \) at \( x = 0 \).
If the tangent to a curve is parallel to the x-axis, what is its slope?
The slope of the normal to the curve \( y = x^3 \) at \( x = 1 \) is:
Sample Questions
The slope of the normal to a curve at a point is the negative reciprocal of the slope of the tangent.
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True
By definition, the normal is perpendicular to the tangent. If tangent slope is \( m \), normal slope is \( -\frac{1}{m} \).
For the curve \( y = \sin x \), what is the slope of the tangent at \( x = 0 \)?
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1
Differentiate: \( \frac{dy}{dx} = \cos x \). At \( x = 0 \), \( \cos 0 = 1 \).
The equation of the tangent to \( y = x^2 \) at \( (1, 1) \) is:
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y = 2x - 1
Slope at \( x = 1 \) is 2. Using point-slope: \( y - 1 = 2(x - 1) \Rightarrow y = 2x - 1 \).
The length of the subnormal to the curve \( y^2 = 4ax \) is constant.
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True
For \( y^2 = 4ax \), \( yy' = 2a \), so subnormal = \( |yy'| = 2a \), a constant.
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