Find the equation of tangent line to the curve y = x2 – \sqrt[3]{x} at the point (-1,0).
SOLUTION :
y = x^2 - cube root(x) = x^2 - x^(1/3)
So, slope of the tangent = dy/dx = 2x - 1/3 x^(- 2/3)
At point (- 1, 0) the slope = dy/dx at x = - 1, is :
= 2(-1) - 1/3 (-1)^(-2/3)
= - 2 - 1/3 * 1/((-1)^(2/3))
= - 2 - 1/3 * 1/(-1)^2
= - 2 - 1/3
= -7/3
So, equation of the tangent at point (- 1, 0) is :
y = - 7/3 x + c
As point (- 1, 0) is both on the curve and the tangent :
=> 0 = - 7/3 (-1) + c
=> c = - 7/3
So,
Equation of the tangent at point (-1, 0) is :
y = - 7/3 x - 7/3 (ANSWER).
Find an equation for the tangent line to the curve at the given points. y = x2 – 5x + 4 at the intercepts (1,0),(4,0), and (0,4). y = at (1,0) y= at (4,0) y = at (0,4) Sketch the curve and the tangent line. VA VA X 4 Submit Answer
Find an equation for the line that is tangent to the curve y = 3x3 - 3x at the point (-1,0). The equation is y=1 (Type an expression using x as the variable.)
1. Find the equation of the tangent line to: a) y = x2 – 3 at the point (2,1) b) y = cos x at the point (1,1) c) y=e" at the point where r = 1 d) r3 + y3 = 19 at the point (3,-2) 2. Find the equation of the normal line to: a) y = r at the point (2,8) b) y=x+ at the point where x = 2 c) y = 2:03 - 5x +...
The equation of this Find the equation of the tangent Line to the curve y = 6 tan z at the point (536). tangent line can be written in the form y = mx + b where mis: and where bis:
find an equation for the tangent to the curve at the given point. y=x2 -x (3,6)
Find an equation of the tangent line to the graph of y = In(x2) at the point (4, In(16)). y =
Find an equation of the tangent line to the curve at the given point. y = x4 + 5x2 - x, (1,5) y = Show My Work (Requiredi 2
Find an equation for the line tangent to the curve at the point defined by the given value of t. x = sin t, y = 2 sin t, t = wa y = 2x - 213 y = 2x y = 2x + 13 Oy=-2x+ 2/3 Find an equation for the line tangent to the curve at the point defined by the given value of t. x=t, y= V2t, t = 18 y=- X-3 y=+x+3 O y = 1...
d²y Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point dx x= 16 cost. y = 4 sint, t = 7 л 2 The equation represents the line tangent to the curve att (Type an exact answer, using radicals as needed.) dy The value of att is dx? (Type an exact answer, using radicals as needed.) 70 4
4. Find the equation of the tangent line to curve 3 (x2 + y2) ? = 25 (x2 - y2),= 1 at (2,1).