Question
The point on the curve $y=x^{2}-2 x+3$, which is closest to the straight line $y=2 x-2$ is(a) $(3,6)$(b) $(2,3)$(c) $(-2,11)$(d) $(1,2)$
Step 1
The derivative of the curve gives the slope of the tangent at any point on the curve. So, let's find the derivative of the curve. \[y'=2x-2\] Show more…
Show all steps
Your feedback will help us improve your experience
Malika Singh and 94 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The point on the curve $3 x^{2}-4 y^{2}=72$ which is nearest to the line $3 x+2 y+1=0$ is (A) $(6,-3)$ (B) $(6,3)$ (C) $(-6,3)$ (D) $(-6,-3)$
The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is (A) $(2 \sqrt{2}, 4)$ (B) $(2 \sqrt{2}, 0)$ (C) $(0,0)$ (D) $(2,2)$
Application of Derivatives
Approximations
The points on the curve $x y^{2}=1$ which are nearest to the origin are (A) $\left[\left(\frac{1}{2}\right)^{1 / 3}, \pm\left(\frac{1}{2}\right)^{-1 / 6}\right]$ (B) $\left[\left(\frac{1}{2}\right)^{1 / 3}, 2^{-1 / 6}\right]$ (C) $\left(2^{1 / 3}, \pm\left(\frac{1}{2}\right)^{-1 / 6}\right)$ (D) None of these
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD