Bài tập CALCULUS 06

Created by T Madas Question 20 (**+) The curve C has equation y = − x ( x + 1) , x ∈ » The curve meets the coordinate axes at the origin O and at the point A a) Sketch the graph of C , indicating clearly the coordinates of A b) Show that the straight line with equation x + y +1 = , is a tangent to C at A C1D , A ( −1, ) Created by T Madas Created by T Madas Question 21 (**+) y = x ( x − 5) y O x A fish logo is generated by the curve C with equation y = x ( x − 5) , ≤ x ≤ , and its reflection in the x axis The curve C meets the x axis at the origin O and at the point ( 5,0 ) The finite region R is bounded by C , its reflection in the x axis and the straight line with equation x = Show that the area of R , shown shaded in the figure, is 54 square units MP1-N , proof Created by T Madas Created by T Madas Question 22 (**+) A curve C has equation y = x3 − 3x − 24 x − , x ∈ » Find the range of values of x , for which y is increasing C2N , x < −2 ∪ x > Question 23 (**+) y = x , x∈», x > Show clearly that d2y dx + dy = y dx C1O , proof Created by T Madas