Calculus I: Lesson 6: Finding the Equation of a Tangent LineDr. Karen Brucks
Calculus: Tangent Line 保存副本 登录注册 fx=lnx+1 1 gx=ddxfx 2 a=−1 −1 10 3 y=gax−a+fa 4 a,fa 标签 5 6 技术支持 x y a2 ab 7 8 9 ÷ 功能 ( ) < > 4 5 6 × |a| , ≤ ≥ 1 2 3 − A B C
11. One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point (2, 4) on the graph of the quadratic function f(x) = x2.A5+4+(2,4)3+21T X-3-2-112 3(b)Find the slope of...
For the above quadratic function to have one solution only, it needs to have its discriminant D equal to zero.D = 16 - 12 p = 0Solve the above for p to findp = 4 / 3b) To find the value of x where the horizontal tangent line occurs, we need to solve the above quadratic equati...
3.2.1 The Slope of a Tangent Line 3.2.2 Instantaneous Rate 3.2.3 The Equation of a Tangent Line 3.2.4 More on Instantaneous Rate 3.3 Some Special Derivatives 3.3.1 The Derivative of the Reciprocal Function 3.3.2 The Derivative of the Square Root Function ...
1.1RatesofChangeandLimits TheTangentProblemLetfbeafunctionandletP(a,f(a))beapointonthegraphoff.TofindtheslopemofthetangentlinelatP(a,f(a))onthegraphoff,wefirstchooseanothernearbypointQ(x,f(x))onthegraph(seeFigure1)andthencomputetheslopemPQofthesecantlinePQ.mpQ f(x)f(a).xa 0 ...
(b) Write an equation for the line tangent to the solution curve that passes through the point (−1, 4). (c) Find the particular solution = () to the differential equation with the initial condition (−1, 4). 9. Craig is traveling east-west along a straight path. Craig’s ...
Calculus: Tangent Line 保存副本登录注册 表达式1: "f" left parenthesis, "x" , right parenthesis equals sine left parenthesis, "x" , right parenthesis plus .3 "x" 有图表。 要进行音频跟踪,按“Alt 键 + T”。fx=sinx+.3x 1 表达式2: "g" left parenthesis, "x" , right parenthesis equals...
line5x–2y10. 2.Solvetheinequality3|2x–4|6graphically.Writethesolutionininterval notation. 2 3.Givenf(x)x+1,evaluate. 4.Solveforx:4lnx–26. 3 5.Givenf(x)x–8andg(x)2x–2,findf(g(2)). Chapter6 6.Afunctionfiscontinuouson[–2,0]andsomeofthevaluesoffareshown ...
Integral calculus, by contrast, seeks to find the quantity where the rate of change is known. This branch focuses on such concepts as slopes of tangent lines and velocities. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space or areaunderthe ...