Find the derivative. 1) f(x)= V7,7x A) 7.7)4/5 B) 7.7)-1/56 ,7) D) 2) y = x/10x-8 15x-8 A) 15x B) 10x-8 21x- 16 D) V10x-8 10х- 8 210x-8

Q: Find an equation of the tangent line to the curve y = 2x +3 that is parallel to the line 8x y+3 = 0.

A: Find an equation of tangent line to the curve y=2x2+3 that is parallel to the line 8x-y+3=0

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: Find the equation of the tangent line to y = 2"-5a -5x+1 = 4. at x = y = 12 In 2 - 1

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Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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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 an equation of the tangent line to the curve y=2x^2+3 that is parallel to the line 8x-y+3=0

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Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

A:

Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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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: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the equation of the tangent line to the curve y=5x²-1 at x= -1. Y=15x + 9 Y=15x-6 O y= x-6 O…

A: Topic:- application of derivatives

Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

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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: Find the equation of line tangent of y=x4-2x2+1 at (2,9)

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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: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: Find the derivatives of the functions in Exercises 27. y = x2sin^2 (2x2)           28. y = x^-2sin^2…

A: To find derivative of 1) y=x2sin2(2x2)2y=x-2sin2(x3)

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

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Q: 3. Determine the gradient of the tangent at a point (2, 5) to the XY graph with the implicit…

A:

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

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Q: Find the equation of the tangent line to y = 2r5 - 3x³ at the point where x = 0.7, with coefficients…

A: Methods to find the equation of the tangent at a point helps to find the required answer to the…

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: 7. Find the slope of the line tangent to the curve at the point (2,1). x²y + xy² = 3x %3D

A: 7. The equation is given by x2y+xy2 = 3x                                                ......(1)…

Q: Find the equation of the tangent line to 4x2 +y2= 8 at (1,2)

A:

Q: With respect to u, what is the derivative of: * 12 בV 2 2 dx Option1 Option3 -'/2 -15

A: Answer is mentioned below -

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: Find the x-coordinate of the point/s on the curve y = 2x – 3x² – 12x + 20 where the tangent line is…

A: The slope of the tangent line to the curve at point P(x,y) is given by,…

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 27 –14a5 –30z² +36x –8 2y5 -2x+2 dy %3D dæ 27+15* –…

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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: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: 11. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? %3D a. -5 b. -6…

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Q: #4. Find the equations of the tangent lines to the relation 3y = x² - 4y when x 2.

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

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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: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: What is the equation of the tangent line to the curve f(x)= 4x2 + 2x -1 at the point x=0 ?  a.)…

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Q: Find the derivative of the function. 4x - 5 8x + 1 dx dx d (8x + 1) • (4x - 5)– (4x – 5) • d (8x+1)…

A: Explanation of the answer is as follows

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.