# Slope of a Curve at a Point

The slope of a curve at a point is a fundamental concept in calculus, providing insight into the rate of change of a function at a specific location. It captures the steepness or inclination of the curve precisely at that point, offering a dynamic understanding of how the function evolves locally. Through the derivative, a mathematical tool central to calculus, the slope at a given point becomes a tangible measure, facilitating the analysis of various real-world phenomena and mathematical models. This concept plays a pivotal role in grasping the intricate dynamics of functions, serving as a cornerstone in calculus applications.

Questions

- How do you find the slope of the tangent line to the graph of the function #f(x)=3/2x+1# at (-2,-2)?
- How do you find the slope of the tangent to the curve #y = 3 + 4x^2 - 2x^3# where x = a?
- How do you find the slope of a curve at a point?
- How do you find the slope of the tangent line to the graph of the function #f(x)=3-2x# at (-1,5)?
- What is the slope of #f(x)=-xe^x/x^2# at #x=1#?
- What is the slope of #y=4x-3# at #x=-1#?
- What is the slope of #f(x)=xe^(x-x^2) # at #x=-1#?
- How do you find a parabola with equation #y=ax^2+bx+c# that has slope 4 at x=1, slope -8 at x=-1 and passes through (2,15)?
- How do you find the slope of the tangent line to the parabola #y=7x-x^2# at the point (1,6)?
- How do you find the slope of the graph #f(x)=(2x+1)^2# at (0,1)?
- How do you find the slope of the graph #g(t)=2+3cost# at (pi,-1)?
- How do you find the slope of the secant lines of #f(x)=x^3-12x+1# through the points: -3 and 3?
- Use the limit definition to find the derivative of f(x)=3/sqrtx at the number a, and use it to find the equation of the tangent line to the curve at the point (1,3)?
- How do you find the slope of the secant lines of # f (x) = x^2 − x − 42# at (−5, −12), and (7, 0)?
- How do you find the slope of the secant lines of #f(x) = 2/x + 2# through the points: (0, f(0)) and (0+h, f(0+h))?
- The curve Y= X^3-3x has a slope 3 at two points. Find the two points?
- At what points on the graph of #f(x)=2x^3-9x^2-12x+5# is the slope of the tangent line 12?
- How do you find the slope of the tangent line to the graph of the function #f(x)=x^2-4# at (1,-3)?
- How do you find the slope of the graph #f(x)=3x^3-6# at (2,18)?
- How do you find the slope of the secant lines of #f(x) = sqrtx# at P(4,2)?