Find the slope of the curve y=x4 at x=3.

Q: Find the equation of the line tangent to the curve y=x-x^2 (x squared) at x=-4

A:

Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

A:

Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

A:

Q: Find the slope of the tangent line to the curve - 3a? + xy + 3y³ = 45 at the point (– 3, 3).

A:

Q: Find an equation of the curve that passes through the point (0, 2) and whose slope is xy?

A:

Q: find the slope of the curve at the point indicated.

A: We need to find the slope of the curve at the point indicated, y=5x-3x2,x=1

Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

A: v

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: At what point(s) on the curve x = (x, y) = 6t² + 4, y = t³ - 7 does the tangent line have slope?

A: This question is related to parametric curves and slope of tangent, we will solve it using given…

Q: Find the slope of the curve 1 at the point P (2, ;).

A: Explanation of the answer is as follows

Q: Find the slope of the curve x2 + y3 = 2 at each point wherey = 1

A:

Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

A:

Q: Find the equation of the line tangent to the curve 3t2 + 8,y = 8t + 3 at t = 2

A:

Q: Find the slope of the tangent to the curve y=4/(5-4x) at x1=9

A:

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

A:

Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

A:

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: Determine slope of a curve y = x³3 + 1 at x = 1

A:

Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

A:

Q: The slope of the curve y = (5x² + 8x + e)eje at x = 0 is

A:

Q: Determine the values of x where a curve y=x³-3x²-9x+12 has horizontal tangent lines

A: Given,y=x3-3x2-9x+12differentiating both the sides w.r.t. xdydx=ddxx3-3x2-9x+12dydx=3x2-6x-9

Q: Find the equation for the line tangent to the curve 2exy = x + y

A:

Q: Differentiate implicitly to find the slope of the curve at the given point. y3 + yx2 + x2 - 3y2 = 0;…

A:

Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

A:

Q: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

Q: Find the equation of the line tangent to the curve x = 3t2 + 8 , y = 8t + 3 at t = 2

A:

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Differentiate implicitly to find the slope of the curve at the given point. 3-y3=D5; (3,5) %3D 0 2…

A: We have to find the slope of the curve at the given point. For this we will find derivative dydx…

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: At what point on the curve x = 9t2 + 3, y = t3 – 2 does the tangent line have slope ? (x, y) =

A:

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the slope of the tangent to the curve y=2/(8-5x) at x1=6.

A: Calculate the differentiation:-

Q: Find the slope of the tangent line to the curve - l2? – 2ay + 4y³ = - 249 at the point (1, – 4).

A:

Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

A:

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: find the slope of the curve at the point indicated y = x - 1/x + 1, x = 0

A: Given, y=x-1x+1 and the point x = 0

Q: Find the points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

A:

Q: What is the slope of the line tangent to the curve  y=7cosx when x=π/4?

A:

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.

Q: At what point(s) on the curve x = 3t2+1, y= t3 -1 does the tangent line have slope?

A:

Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

A:

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,