By Bob Miller

**With Bob Miller at your part, you by no means must be clueless approximately math again!**

Algebra and calculus are difficult on highschool scholars such as you. Professor Bob Miller, with greater than 30 years' instructing adventure, is a grasp at making the advanced basic, and his now-classic sequence of Clueless research aids has helped tens of millions comprehend the cruel subjects.

Calculus-with its integrals and derivatives-is well-known for tripping up even the fastest minds. Now Bob Miller-with his 30-plus years' adventure instructing it-presents highschool calculus in a transparent, funny, and interesting way.

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**Additional info for Bob Miller's high school calculus for the clueless : high school calculus : honors calculus, AB and BC calculus**

**Example text**

M ϭ yЈ ϭ 2x ϩ 4 ϭ 2(2) ϩ 4 ϭ 8. y ϭ (2)2 ϩ 4(2) ϩ 7 y Ϫ 19 ϭ 19. The line is 8 ϭ . xϪ2 C. m ϭ 2x ϩ 4. Since x2 ϩ 4x ϩ 7 ϭ 12, x2 ϩ 4x ϭ 5 ϭ 0 or (x ϩ 5)(x Ϫ 1) ϭ 0. So x ϭ 1 and x ϭ Ϫ5. The points are (1, 12) and (Ϫ5, 12). For the point (1, 12), m ϭ 2(1) ϩ 4 ϭ 6 and the y Ϫ 12 equation of the line is 6 ϭ x Ϫ 1 . For the point (Ϫ5, 12), m ϭ 2(Ϫ5) ϩ 6 ϭ Ϫ4 and y Ϫ 12 the equation is Ϫ4 ϭ x ϩ 5 . Here’s the picture: See, there are two lines where y ϭ 12. y (– 5, 12) L1 (1, 12) y = 12 L2 x The Basics D.

The example is then virtually the same as Example 15. Now seems to be a fine time to insert problems you are likely to see. They are written in roughly increasing order of difficulty. EXAMPLE 21— A. Find the equation of the line tangent to y ϭ x2 ϩ 4x ϩ 7 at the point (1, 12). B. Find the equation of the line tangent to y ϭ x2 ϩ 4x ϩ 7 if x ϭ 2. C. Find the equation of the lines tangent to y ϭ x2 ϩ 4x ϩ 7 when y ϭ 12. D. Find the equation of the line tangent to y ϭ x2 ϩ 4x ϩ 7 that is perpendicular to the line 5x ϩ 10y ϭ 11.

Since everything on P2Q has the same x value, the length of P2Q ϭ y2 Ϫ y1. The slope is mϭ y2 Ϫ y1 change in y ⌬y ϭx Ϫx ϭ ⌬x 2 1 change in x ⌬ ϭ delta, another Greek letter Let’s do the same thing for a general function y ϭ f(x). The Basics Let point P1 be the point (x, y) ϭ (x, f(x)). A little bit away from x is x ϩ ⌬x. ) The corresponding y value is f(x ϩ ⌬x). So P2 ϭ (x ϩ ⌬x, f(x ϩ ⌬x)). As before, draw a line through P1 parallel to the x axis and a line through P2 parallel to the y axis. The lines again meet at Q.