For the curve f (x) = -2(3)" +3, the y-intercept occurs at:

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

A:

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

A:

Q: 2. Find the tangent lines to the curve y = x4 – 14x2 + 17x + 40 perpendicular to the line x = 7y +…

A: Given, y=x4-14x2+17x+40 Now differentiate with respect to x we get, dydx=4x3-28x+17 The tangent is…

Q: Find the points on the curve 9y = x where normal to the curve makes equal intercepts with the axes.

A: Since, the equation of curve is given by 9y2=x3-(i)⇒y2=x39⇒y=±x33Differentitaing equation-(i) both…

Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

A:

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: Find the equation of the tangent line to the curve y2=6x-3 perpendicular to the line x+3y=7

A:

Q: What is the equation of the line tangent to the graph of y = 2x³/2 at the origin? Oy=0 Oy = 2r Oy =…

A:

Q: Find the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

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Q: Find the equation of a line tangential to the curve y = 2x² + 7x + 9 at P(1,18).

A:

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find an equation for the line tangent to given curve y = -10z2-3 4r+1 3 at x = 0-

A:

Q: Find the points on the curve y = 2r3 – 3x2 – 12x + 20 - where the tangent is parallel to the x-axis.

A: A straight line parallel to x-axis have slope 0.

Q: Find the equation of the line that is tangent to the curve r = x In y, x > 0, at the point (1,е).

A: Equation if the line (y - y1) = m(x -x1) D(uv) = uDv + vDu , where D is the differentiation of…

Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: Find the length of the curve y = 1 - e^-x, 0 <=x<=1.

A: The given curve is

Q: Determine the slope of the curve x2+ y2– 6x – 4y – 21 = 0 at (0, 7).

A:

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find the equation of the line tangent to the curve x = 3t2 + 8 , y = 8t + 3 at t = 2

A:

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: B. Find the length of the curve y = x² from x 0 tox = 4.

A:

Q: Find the slope of the tangent line to the curve Ar 3ay + 2y°= 3

A: Given,         The curve is 4x2-3xy+2y3=3 at the point 1,1.

Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

A:

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

A:

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: Find the equation of the tangent to the curve y 18x- 2y-3 0. 3e3 that is parallel to the line

A:

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: Determine the slope of the curve x2 + y2 – 6x – 4y – 21 = 0 at ( 0, 7 ).

A:

Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: The curve y = -x² + x + 1 opens: A. Upward %3D B. To the left C. To the right D. Downward

A: Given that the curve is         y = -x2 +x +1 Here we have to show that the curve opens in which…

Q: Find the length of the curve y = x^4 for 0&lt;_x &lt;_1

A:

Q: Find the equation of the line normal to the curve 2x^2-3xy+y-18=0 at (3,0).

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.