V1 – x2 f'(x) =

Q: Find an equation of the tangent plane at the given point: (2,1) F(r.a) 3²-3,

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Find the equation of the line tangent to the curve 8x4 + 8y² = 16 at the point (1, 1).

A: To find the equation of the line tangent to the curve 8x4+8y2=16 at the point 1, 1.

Q: 3. Find the equation of the tangent line to the graph of x²y? + 9xy = 162 at the point (-3, 6).

A:

Q: Find the points on the curve t² 16t+ 6, y X = = A. a horizontal tangent line B. a vertical tangent…

A: Given the curve is x=t2-16t+6  and y=t2+4t+3

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: 3. Sketch the curve: y = (x²–1)(x+2) x-3

A: y=(x2-1)(x+2)(x-3)y=(x-1)(x+1)(x+2)(x-3)X-intercept:(-2, 0), (-1, 0), (1, 0)Y-intercept:(0, 23)…

Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

A:

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: Assume that a rocket is in space and is following the path y = – 6(x − 7)² + 3, from left to right…

A:

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: A mouse Q runs along the positive y-axis at the constant speed v at the origin. A cat P chases the…

A: It is given that∙Mouse Q runs along y-axis with a constant velocity v1∙Cat P runs along curve C with…