The function T(x)= ax^2 +bx + c  has the values T(0)= -4, T(1)= -2, and T(2)=6. Find a, b, and c.

Q: The first derivative of f(x) = (5x – 6x)-3 will be.

A: Solution of first derivative

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: Find the first and second derivative if 1 w = 3z-2 ミ

A:

Q: Find the partial derivative. 3 (x² +3x-3y) 2.

A: Given  z = x2+3x-3y4 We have to find ∂z∂x.

Q: Find the derivative. y = 5x 4 - 5x 3 7 O 4x3 + 3x2 O 20x3 - 15x2 - 7 O 4x3 + 3x2 - 7 O 20x3- 15x2

A: Given,  y = 5x4 -5x3-7  We have to find the derivative of  y = 5x4 -5x3-7

Q: Find the derivative of y = 2 + v2 + vx5 |2 + V2 + Vx5

A:

Q: FInd the derivative of y=(5x-3)5(2-x4)5

A:

Q: f(x) = (6x² - 2x+1)^

A:

Q: What is the first derivative of 2x^2 + 3x + 5

A: find differentiation:-

Q: Solve for the second-order derivative of: [(4x3-1)(8x2+6x-3)]3

A: We have to calculate second order derivative of [(4x3-1) (8x2+6x-3)]3   Let us say  Y= [(4x3-1)…

Q: 10x-9y-0-11 the same as -10x-9y+11? Or is it just -10x-9y-11 when finding Partial Derivative?

A: Reprieve is to clarify the doubts.

Q: Find the derivative of f (x) = V3x² In(3x²). 2/3x2 A 3x In(3x²) + V3x2 2 + 3x In(3x²) В

A: Given thatfx=3x2ln3x2To find : derivative of…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the derivative of y = 3x² + 5x- 2 from first principles.

A:

Q: Find the derivative of (2x^3+3x+1)^1/3

A:

Q: Calculate the derivative of the exercise: y=(4x3+3)4(x+1)-3

A: To find: The derivative of below expression.

Q: Find the first derivative: y= In V5x3 - 2

A: Given: y=ln5x3-25 We need to evaluate dy/dx. This can be done as follows:

Q: f(x)= (7x¹-5x-2)

A:

Q: find the first and second derivatives

A: Given expression: w=3z7-7z3+21z2

Q: Find the First derivative of 5x/2 4x %3D

A:

Q: Find the derivative of sech(2x1/9)

A:

Q: The fourth derivative for * 3 points y = x3 - 3x2 + 2 are 6x-6

A:

Q: Write a derivative formula for the function fx)- 12.2(4.7 x2 1.5475x(4.7-2( 4.7*) f'(x) 12.2 = X

A: Given

Q: =) f(x) = x²e¬4x

A:

Q: ƒ(x) = (x³ – 4x) 10

A: Solve the derivative

Q: 4 6. ν- x3

A:

Q: Find the equation of the line tangent to f(x)=3x2 +4x+5 at the point (0, 5)

A: Given : f(x) = 3x2 + 4x + 5 A point (0, 5)   To  find the equation of the tangent line.

Q: A cigar manufacturer produces x cases of cigars per day at a daily cost of 50x(x + 200)>(x + 100)…

A:

Q: If y = csch4 2x°, find the 1st derivative a. 20x*csch42x° coth 2x5 b. -40x4 csch4 2x° coth 2x c.…

A: Some derivative formulas: ddx(f(x)g(x))=f(x)ddxg(x)+g(x)ddxf(x) ddx(u(v(x)))=u'(v(x))ddxv(x)…

Q: Find the first derivative of -5x²+2x-5 210x -5x²+2x-4 ебх о о 5x2-2x+5 P5х 2 x2+1 e5x

A:

Q: A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A…

A: Linear equations

Q: 6. 3. Find the derivative of: -2Vx++ 5x – 8

A:

Q: Suppose the percent of males who enrolled in college within 12 months of high school graduation is…

A: Given:         Percent of males enrolled in college is    y= -0.126x + 55.72         Percent of…

Q: Find the derivative. Using Chain Rule y = (2x2 – 1)3(3x² + 1)³ |

A: According to question,Given Function,y = 2x2-133x2 + 13

Q: Find the 3rd derivative of y=(x³-2x)².

A: y=x3-2x2 Differentiating with respect to x, we get dydx=2x3-2x·dx3-2xdx=2x3-2x·3x2-2 Again…

Q: 9) Find the value of the derivative at the point (2,-18) ƒ(x) = -3xV2x + 5

A:

Q: Find the First derivative of 2(x-2)^2 (x+3)^2

A: Given, y=2x-22x+32

Q: Find the derivative for ()= 2z²+9 %3D 3-5z

A: Consider the function

Q: Ax) = (5 – 3x²)"V6x² - 6x = 8x – 12

A: Given: fx=5-3x276x2+8x-12 To Find: The derivative of the given function

Q: A rectangle’s length is growing at 3 inches per second, while its width is shrinking at 5 inches per…

A:

Q: Find the derivative of f (x) = – 5x 5z) (-² + 6x – 6 ) . -

A:

Q: Find the first derivative: y = In V2x3 -5 222 O y' = 2z3-5 5z2 O y' = 223-5 3z2 O y'= %3D 223-5 O y'…

A: Using Chain rule Y= f(g(x))  so Y' = f'(g(x))•g'(x)

Q: find the critical points and apply the Second Derivative Test (or state that it fails). y = 6x^3/2 −…

A:

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A:

Q: Find the first and second derivative if y=4-2x-x-3

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.