Question

At what points on the given curve x = 4t^3, y = 4 + 64t - 16t^2 does the tangent line have slope 1? (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value)

          At what points on the given curve x = 4t^3, y = 4 + 64t - 16t^2 does the tangent line have slope 1?
(x, y) = ( ) (smaller x-value)
(x, y) = ( ) (larger x-value)

Added by Christopher Q.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/11/2022

Step 1

We know that X = 4t^3, so we can find dx/dt = 12t^2. Similarly, Y = 4 + 64t - 16t^2, so dy/dt = 64 - 32t. The slope of the tangent line is given by dy/dx, which is (dy/dt) / (dx/dt). So, dy/dx = (64 - 32t) / (12t^2) = (32(2 - t)) / (12t^2) = (8/3)(2 - t) / Show more…

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