ge shown below represent a curve (in black color) of quarter arde, knowing that this curve starts from pl toward p0, and the tangents meet at point P2. What is the value of in terms of p S P(U) = [2u - 3u +1 -2u³ +3u² u? - 2u² + u u? – u²] po !!

Q: graph of flx)= Inlx) concave down 7

A:

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: 4) Solve the following linear system or indicate the nonexistence of solution. X1 – 2x2 + 5x3 – 3x4…

A: Or, take x2 = k Hence, solution of the system is x1 = 1+2k, x2 = k, x3 = 1, x4 = 2

Q: What is the slope of the tangent line to the curve xy +y– 1=0 at the point (0, 1)? -1 -3 -2 1

A:

Q: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

Q: Find the point where the tangent to the curve y = x +6x + 9x + 7 is parallel to the x-axis. 37.…

A: topic - point at which tangent line is parallel to curve. note : As per bartleby guidelines, we are…

Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: 1. a) Find dy for the equation 4x²y ² - x ³y = 3 dx b) find the x-coordinate of each point on the…

A:

Q: Give an equation for the tangent line to = 1 at the y2+1 point (5,2) and sketch it on the graph. -5-…

A:

Q: B. Find the slope of the curve at the given point. Ax = 4u(2 – 3u)², y = 3u² – 4u + 4 u =

A:

Q: c) Find the equation of the tangent line to the function y = sec²x at the point (2:2).

A: Given function as y=sec2x

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.