(a) If Q is the point ( x, ,find the slope of the secant line PQ (correct to six d 3 - x (i) 3.9 mpQ (ii) 3.99 (iii) 3.999 mpQ (iv) 3.9999 (v) 4.1 MpQ (vi) 4.01 (vii) 4.001 (viii) 4.0001 ||||||||

Q: Differentiate implicity to find the slope of the following curve at (0,3) x^3+yx^2+x^2-3y^2=0

A:

Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: What is the slope of the tangent line of y = 3x- 2x2 + 2x -5 at x = 0? A. 2 B. -5 C. D.

A: Given equation of the curve is y=3x3-2x2+2x-5   x=0 find slope of the tangent

Q: 12. Determine the y-intercept of a line with a slope of -2 that is a tangent to the curve: y =…

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Q: 1) What is the slope of the graph y = 5e³x at x = 1?

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Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: :-1 What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point…

A: As per guidelines we have to solve the 1st one

Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: 9. What is the slope of the curve at the given point? Sx² + 2.ry – y² = -3 at (.2)

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Q: 2. Estimate the slope of Ix) at the point: a) where x = 3 b) where x = 2 YA fx) 4 3 2 1 2 3 4 5 6 1.

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Q: tangent to the curve x^3 +x^2 y + 4y - 1 + 0 at the point (3,-2) has a slope equal to: a. -13/15…

A: We will find the slope.

Q: 2. (6 marks) Find the slope of the line tangent to f: y = 2/5x + 1 at the point (3,8). c) - D) E) -…

A: Answer and explanation is given below..

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: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: Find the equation of the tangents to the graph y = x^3 + 3x^2 - 15x -20 at Ox-y-9=0 O9x-y-48 = 0 O9y…

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Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

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Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: B. Find the slope of the curve at the given point. 1. y = 4 – 3x2 at (-1, 1) 2. y = x2 – 5 at (1,…

A:

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: If the line 3x - 4y = 0 is tangent in the first quadrant to the curve y = x^3 + k then what is the…

A:

Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

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Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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Q: Differentiate implicitly to find the slope of the curve at the given point. y3 + yx2 + x2 - 3y2 = 0;…

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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: Are there any points on the curve y = x - e^-x where the slope is 2? If so, find them.

A: To determine the point where the slope of the function is 2.

Q: End the Vellue of g) if the slope of the Curve y= x-2x is (2)?

A:

Q: If the slope of an arbitrary curve y=f(x) at a point p0(x0, f(xo)) is S. So do you think the slope…

A:

Q: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: What is the approximate slope of the curve with equation f(x)=(1/x-1) at x = 1.2?

A: To find the approximate slope of the curve with equation f(x)=(1/x-1) at x = 1.2

Q: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

Q: What is the slope of the secant line that intersects the graph of h(x) = 16 – z at z = l and a = 4?

A: The slope of the secant line or any other line can be defined as the rise to the run ratio which is…

Q: 7x Find the points on the graph y = x-2 - where the slope of the tangent line is parallel 28x +50y –…

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Q: If f'(4)= 6 and g'(4)=3, then the slope of the tangent line to the graph of y=2f(x)-5g(x) at x=4 is…

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Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

A:

Q: If y=mx+b is the equation of the tangent line the curve y=x2-3x+5 , which is parallel to the secant…

A: Proceed as shown

Q: Find the points on the graph of x5/2 + y5/2= 1 where the slope of the tangent line is -1.

A: Topic:- application of derivatives

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find the values of a and b if the tangent to y = ar² + bx at (1,5) has a slope of 8.

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Q: If the curve is defined by y= x⁴ - 8x³ + 22x²-24x+9, then what are the value/s of x for which the…

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Q: 2. Find the slope of the curve y = 3x +1 at the point (-0). Draw the graph of the curve.

A: GIVEN y2=3x+1 at(-1/3,0) we need to find the slope of the curve and graph the curve

Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

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

A: x2-xy+y2=36

Q: Identify the slope from the line of best fit y = |- 0 NIN 31 0-²

A: Solution-: The given regression line is  y=27-13*x We want find the slope of the regression line

Q: 15.)) What is the slope of the line tangent to the curve y +2 = - 2sin y at the point (2, 0)? 2 (A)…

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Q: 49. Find the slope of the curve y = (2x2 - x+ 3)(x + x+1) at (1, 12).

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Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,