(c) Is f differentiable at x = 1? 4. (a) Show that the equation of the tangent line graph of the parabola y = f(x) = x² at the point P₁ = (t, t²) is given by: y = 2t x-t² 2 Hint: Recall that from the point-slope form this line must have equation of the fo

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(c) Is f differentiable at x = 1?
4. (a) Show that the equation of the tangent line to the
graph of the parabola y = f(x) = x²
at the point P₁ = (t, t²) is given by:
y = 2t x-t²
Hint: Recall that from the point-slope formula,
this line must have equation of the form:
y t² = f'(t).(x-t).
(b) For which values of t will the tangent line at
Pt = (t, t²) pass through R = (-1,-3)?
(c) What are the coordinates of the points
P and Q on the parabola?
y=x²
R
P
slope = f'(t)
P₁ =(t,t¹)
X
Transcribed Image Text:(c) Is f differentiable at x = 1? 4. (a) Show that the equation of the tangent line to the graph of the parabola y = f(x) = x² at the point P₁ = (t, t²) is given by: y = 2t x-t² Hint: Recall that from the point-slope formula, this line must have equation of the form: y t² = f'(t).(x-t). (b) For which values of t will the tangent line at Pt = (t, t²) pass through R = (-1,-3)? (c) What are the coordinates of the points P and Q on the parabola? y=x² R P slope = f'(t) P₁ =(t,t¹) X
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