Q3) Draw the following functions: (3-x, xS1 5, 1sxS0 2x,x >1 1)f(x) = EX 2)y = sec

Q: what is the equation of the tangent line to xy-3y^2=1 at the point (4,1) Express numbers in eaxact…

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Q: To find the length of the curve defined by y = 5x° + 8x from the point (-1,-13) to the point (2,56),…

A: Here the curve is given by y=5x3+8x x coordinate of the points (-1,-13) and (2,56) are -1 and 2…

Q: y = vx² – 9

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Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

A: Given that f(x)=x2 To find two tangents that passes through (-1,-3)

Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (-1,…

A: Here, the given curve is: f(x)=2x2 To find two tangent lines that pass through (-1,-6)

Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

A:

Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: Find equation of the tan gent line to the curve f(x) = /16–4x at (3,2) a)

A: To Determine: a. Find the equation tangent line to the curve

Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: The slope of the tangent line to the graph of f(r) at the point (-7,5) is The equation of the…

A: Topic - equation and slope of tangent line to curve

Q: What points is the function y=|5x-1|+7sin(7x) continuous?

A: we have given function y=5x-1+7sin(7x) we know that  sin(ax) is continuous everywhere hence sin(7x)…

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: Find an equation of the tangent line to the curve y = 2x2 +3 that is parallel to the line 82 – y + 3…

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Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

A:

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Find the slope of line drawn tangent to the function. f(x)=x2+7, at the point (-2,11) by using the…

A: Shape of tangent line to the curve is given by first derivative of curve at given periodDerivative…

Q: Obtain the tangent line of the function y= 2x^2 + 3x + 2 at the point (1,7

A: Given: - The function is, y=2x2+3x+2 at the point (1,7) To find: - The equation of the tangent line…

Q: What is the equation of the tangent line to xy – 3y = 1 at the point (4, 1)? (Express numbers in…

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Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

A:

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

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Q: (A) Find the absolute maxima and minima for y 4x +1 over 3 - [-V5, V5]. (B) Use the second…

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Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

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Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: Find the equation of tangent line to the curve y = 2 - x 2 (7, ²/7). at the point (7, Express the…

A: The objective is to find the equation of tangent line.

Q: Use Secant Method to calculate the root of a function f(x) = e-*(3.2sinx – 0.5cosx) on the interval…

A: To use decant method to calculate the root of a function

Q: 16. r(0) = sec 0 tan 0 – 2eº -

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Q: 1, cosX, cos 2X,--- , cos mx

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Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

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Q: Find a point 2o where the function f (2) = (z – 12 – 12i) (z – 12 – 12i)differentiable. What is the…

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: In the next exercise you have to equal the derivative to zero and then clear x or a y to subtract in…

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Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Find the equation of the tangent line to the function f(x) = 8/x - 2 at the point (64, 62). Provide…

A: To determine the equation of the tangent in the form y =mx+b

Q: 1. Y = 2 – 7.x fa) — 4 — 5х — 21? 2. 3. Y = 2x³ – 3.x

A:

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: