MediumMathematicsHigh School (11–12)Functions and Calculus › Application of DerivativesNumericalA-LevelAPIBJEE Main
Find the point on the curve y = x² + 3x - 5 where the tangent is perpendicular to the line x + 5y =…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find the point on the curve where the tangent is perpendicular to the line . Give the coordinates of the point, and the -intercept of the tangent line there.
Need a reminder? The key ideaShow
A tangent parallel to a line of gradient has . A perpendicular tangent has . For a tangent from an outside point, call the point of contact . The angle between curves satisfies .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The line. gives , so its gradient is .
Step 2. The tangent gradient. It is .
Step 3. The point. gives , and .
Step 4. The tangent. , so . The -intercept is .
Answer: the point is and the -intercept is .
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