Question:
The equation of the tangent to the curve
\[
y = x^3 - 2x + 7
\]
at the point \( (1,6) \) is:
The equation of the tangent to the curve
\[
y = x^3 - 2x + 7
\]
at the point \( (1,6) \) is:
Show Hint
To find the equation of a tangent, differentiate the function and use point-slope form.
Updated On: Mar 24, 2025
- \( y = x + 5 \)
- \( x + y = 7 \)
- \( 2x + y = 8 \)
- \( x + 2y = 13 \)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Finding the derivative
\[
\frac{dy}{dx} = 3x^2 - 2.
\]
Step 2: Evaluating at \( x = 1 \)
\[
m = 3(1)^2 - 2 = 3 - 2 = 1.
\]
Step 3: Using point-slope form
Equation of the tangent:
\[
y - 6 = 1(x - 1).
\]
\[
y = x + 5.
\]
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