Example 1.1. The point P(-2,2) lies on the curve y = √2-x. (1) Sketch the curve and the tangent line at P.

Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

A:

Q: (a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line…

A:

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given: y=5x2+4 ; P3,49 we know that slope at given point 3,49 is given by y'3 so, for finding slope…

Q: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2. if at any point (x, y)…

A: An equation of the tangent line to a curve at the point (3, 5) is y = x + 2.   We have to find the…

Q: Find equations of the tangent lines to the curve y²-xy-6=0 at the points (-1,2), and (-1,-3).

A: Given curve: We have to find the equations of the tangent line to the curve  at the points  and

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+7 and the point (1, 3) is on…

A:

Q: 05:A: Find all points on the curve x²y² + xy = 2 where the slope of the tangent line is -1?

A: Question No. (A): To find all points on the curve where the slope of the tangent line is .Note:…

Q: 8 Find an equation for the tangent line to the graph of y = (x° - 9x) at the point (- 3,0). .....…

A: A detailed solution is given below

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…