Textbook Question
A line perpendicular to another line or to a tangent line is often called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curves at the given point P.
y= √x; P(4, 2)
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2. Intro to Derivatives
Tangent Lines and Derivatives
Back2. Intro to Derivatives
Tangent Lines and Derivatives
- Textbook Question
A line perpendicular to another line or to a tangent line is often called a normal line. Find an equation of the line perpendicular to the line that is tangent to the following curves at the given point P.
y = 2/x; P(1, 2)
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Given the function f and the point Q, find all points P on the graph of f such that the line tangent to f at P passes through Q. Check your work by graphing f and the tangent lines.
f(x)=x²+1; Q(3, 6)
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Given the function f and the point Q, find all points P on the graph of f such that the line tangent to f at P passes through Q. Check your work by graphing f and the tangent lines.
f(x) = 1/x; Q (-2, 4)
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If f′(x)=3x+2, find the slope of the line tangent to the curve y=f(x) at x=1, 2, and 3.
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The line tangent to the graph of f at x=5 is y = 1/10x-2. Find d/dx (4f(x)) |x+5
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Derivatives and tangent lines
a. For the following functions and values of a, find f′(a).
f(x) = 1/ √x; a= 1/4
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Derivatives and tangent lines
b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.
f(x) = 1/ √x; a= 1/4
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Derivatives and tangent lines
a. For the following functions and values of a, find f′(a).
f(x) = 1/ x²; a= 1
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Derivatives and tangent lines
a. For the following functions and values of a, find f′(a).
f(x) = √2x+1; a= 4
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Derivatives and tangent lines
a. For the following functions and values of a, find f′(a).
f(x) = √3x; a= 12
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Derivatives and tangent lines
b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.
f(x) = √3x; a= 12
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Derivatives and tangent lines
a. For the following functions and values of a, find f′(a).
f(x) = 1/3x-1; a= 2
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Derivatives and tangent lines
b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.
f(x) = 1/3x-1; a= 2
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Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.
f(x) = 2x + 1; P(0,1)
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