The parametric form of the tangent line to the image of f(t) = (4t², § , t – 2) at t = 3 is L(t) = | (36-24 t) i + 5/9 ( 3-t) j + ( 1+t ) k

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

Q: Find the slope of the tangent line to the curve cos(За — Зу) — ае -37/2 2 at the point (37/2, 27).

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Q: Find all points on the curve o(t) = (t, t² - t + 3) where the tangent line passes through the origin

A: Yeah we will first find the equation of the tangent line for a general point (for t=a) then we will…

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: Find the tangent plane to the equation z = 2y cos(5z – 4y) at the point (4,5, 10) z = 2y- 2= 0 X…

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Q: Let r be a positive real number. The equation for a circle of radius r whose center is the origin is…

A: Given equation: x2+y2=r2                     . . . (1) (a) Differentiating (1) with respect to x,…

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: 4: In the process of solving the differential equation r'y' - 4x°y = cos(4x), x > 0, which of the…

A: Given differential equation is  x7y'-4x6y= cos(4x)

Q: Let z = (1+z)√√/50 — x² − y². - (A) Calculate the equation of the tangent plane at x = 3, y = 4. (B)…

A: z = (1 + x)50 - x2 - y2 The given function is of the form z = f(x) To calculate the equation of the…

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

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Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: The equation of the tangent line to the curve x² + y? = 9, at (7,-18) is 7 y = 18 7 (х — 7) — 18 18…

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Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

Q: Determine the equation of the line tangent to y = x + tan x at the point (T, T).

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