# Tangent Line to a Curve

The tangent line to a curve is a fundamental concept in calculus and analytic geometry, providing insight into the behavior of functions at specific points. It represents a straight line that touches the curve at a single point, mirroring the curve's slope at that precise location. Understanding tangent lines enables mathematicians and scientists to approximate curves, analyze rates of change, and solve various real-world problems. This concept serves as a cornerstone in calculus, facilitating deeper comprehension of functions, derivatives, and their applications in fields ranging from physics to economics.

Questions

- How do you find an equation of the tangent line to the curve #xe^y+ye^x = 1# at the point (0,1)?
- What is the equation of the tangent line to #f(x)=3-14x# at #x=8#?
- How do you find an equation of the tangent line to the graph of #y = g(x)# at x = 5 if #g(5) = −4# and #g'(5) = 3#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(t) = t − 13 t^2# at t=3?
- What is the equation of the tangent line of #f(x) =arcsin(cosx)# at #x=pi/4#?
- How do you find an equation of the tangent line to the curve at the given point #y=3arccos(x/2) # and #(1,pi)#?
- How do you find the equation of the tangent line to the curve #y=x^3 - 2x# at the point (2,4)?
- The tangent line to the graph of #y=2x^2−3x+1# at the point #P(a,b)# is parallel to the line #y=5x#. This tangent line crosses the x-axis at #(d,0)#. How do I find the value of #d#?
- How do you find the points where the graph of the function #y = x - (x / 18)^2# has horizontal tangents and what is the equation?
- How do you find the equation of the line tangent to the graph of #f(t) = t − 13 t^2#, a = 3?
- How do you find the equation of the tangent line to the curve #y=1+x^3# that is parallel to the line #12x-y=1#?
- How do you show that the curve #6x^3+5x-3# has no tangent line with slope 4?
- How do you find the equation of the line tangent to the graph of #y = sqrtx# at (16,4)?
- What is the equation of the tangent line of #f(x) =tan^2x*sec2x-e^xcosx# at #x=pi/4#?
- What is the equation of the tangent line of #f(x)=e^(-x^2+x+pi)-sinx/e^x# at #x=pi/4#?
- What is the equation of the line tangent to the graph of #f(x)= x^4 + 2x^2# at the point where f ' (x)= 1?
- What is the equation of the line tangent to # f(x)=(e^x-x)^2 # at # x=3#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(x)= 1/(x+2)# at (0,1/2)?
- What is the equation of the line tangent to #f(x)=-x^2 -8x - 1 # at #x=-1#?
- What is the equation of the line tangent to #f(x)=(x-3)^2-x # at #x=-1#?